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Address:
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Current and upcoming events:
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One of my interests earlier on was in L2 Carleman estimates and unique continuation for pde's, as well as their applications in control theory. I have collected together those papers in the Unique Continuation Page. Other more recent papers on unique continuation dealing with Lp Carleman estimates are listed below.
The notes from the Oct 2012 Oberwolfach Seminaire are here, or you can get the entire book at Amazon.
The notes from the Oct 2022 Oberwolfach Seminaire are available from Springer. The lectures from the 2020 summer school "Introduction to water waves", jointly coorganized with Mihaela Ifrim, are available from SLMATH (MSRI). Also more MSRI lectures can be found here.Following are some selected published papers, as well as all the new
preprints. I have tried to loosely and imperfectly organize them by topic, though
several would fit in more than one class. The topics are as follows:
Semilinear dispersive problems.
| On the optimal local regularity for Yang-Mills equations in R4+1 | with Sergiu Klainerman J. Amer. Math. Soc. 12 (1999), no. 1, 93--116. |
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| On the equation u=| ∇ u|2 in 5+1 dimensions. | Math. Res. Lett. 6 (1999), no. 5-6, 469--485 | |
| Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation. | Trans. Amer. Math. Soc. 353 (2001), no. 2, 795--807 | Journal |
| A-Priori Bounds for the 1-D
Cubic NLS in Negative Sobolev Spaces |
with Herbert Koch IMRN 2007, no. 16, Art. ID rnm053, 36 pp. |
arXiv:math/0612717v2 |
| Global well-posedness of the
KP-I initial-value problem in the energy space |
with Alexandru Ionescu and
Carlos Kenig Invent. Math. 173 (2008), no. 2, 265--304. |
arXiv:0705.4239 |
| Global wellposedness in the energy space for the Maxwell-Schrödinger system | with Ioan Bejenaru Comm. Math. Phys. 288 (2009), no. 1, 145--198. |
arXiv:0712.0098 |
| On the 2D Zakharov system with L2 Schrödinger data. | with Ioan Bejenaru, Sebastian Herr and Justin Holmer Nonlinearity 22 (2009), no. 5, 1063--1089. |
arXiv:0811.3047 |
| A convolution estimate for two-dimensional hypersurfaces | with Ioan Bejenaru and Sebastian Herr Rev. Mat. Iberoam. 26 (2010), no. 2, 707-728 |
arXiv:0809.5091 |
| Global well-posedness of the energy critical Nonlinear Schroedinger equation with small initial data in H^1(T^3) | with Sebastian Herr, Nikolay Tzvetkov (2010) Duke Math. J. 159 (2011), no. 2, 329-349. |
arXiv:1005.2832 |
| Strichartz estimates for partially periodic solutions to Schroedinger equations in 4d and applications | with Sebastian Herr, Nikolay Tzvetkov (2010) J. Reine Angew. Math. 690 (2014) |
arXiv:1011.0591 |
| Energy and local energy bounds for the 1-D cubic NLS equation in H^{-1/4} | with Herbert Koch (2010) Ann. Inst. H. Poincare Anal. Non Lineaire 29 (2012), no. 6, 955-988. |
arXiv:1012.0148 |
| Low regularity bounds for mKdV | with Michael Christ and Justin Holmer (2012) Lib. Math. (N.S.) 32 (2012), no. 1, 51-75. |
arXiv:1207.6738 |
| Local wellposedness of Chern-Simons-Schroedinger | with Baoping Liu and Paul Smith (2012) Int. Math. Res. Not. IMRN 2014, no. 23, 6341-6398. |
arXiv:1212.1476 |
| Null structures and degenerate dispersion relations in two space dimensions | with Yuqui Fu (2012) Int. Math. Res. Not. IMRN, (10):7299-7338, 2021. |
arXiv:1801.00099 |
Carleman estimates and unique continuation
| Unique continuation for operators with partially analytic coefficients | J. Math. Pures Appl. (9) 78 (1999), no. 5, 505--521. | |
| Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients | with Herbert Koch Comm. Pure Appl. Math. 54 (2001), no. 3, 339--360. |
pdf |
| Sharp counterexamples in unique continuation for second order elliptic equations | with Herbert Koch J. Reine Angew. Math. 542 (2002), 133--146. |
pdf |
| Dispersive estimates for principally normal pseudodifferential operators. | Comm. Pure Appl. Math. 58 (2005), no. 2, 217--284. | arXiv:math/0401234 |
| Lp eigenfunction bounds for the Hermite operator. | with Herbert Koch Duke Math. J. 128 (2005), no. 2, 369--392. |
arXiv:math/0402261 |
| Carleman estimates and absence of embedded eigenvalues. | with Herbert Koch Comm. Math. Phys. 267 (2006), no. 2, 419--449. |
arXiv:math-ph/0508052 |
| Carleman estimates and unique
continuation for second order parabolic equations with nonsmooth
coefficients |
with Herbert Koch Comm. Partial Differential Equations 34 (2009), no. 4-6, 305--366. |
arXiv:0704.1349 |
| Uniqueness in Calderon's problem with Lipschitz conductivities | with Boaz Haberman (2011) Duke Math. J. 162 (2013), no. 3, 496-516. |
arXiv:1108.6068 |
Wave packets and nonlinear waves
| Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation | Amer. J. Math. 122 (2000), no. 2, 349--376 | |
| Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients. III. | J. Amer. Math. Soc. 15 (2002), no. 2, 419--442 | Journal |
| Sharp counterexamples for Strichartz estimates for low regularity metrics. | with Hart Smith Math. Res. Lett. 9 (2002), no. 2-3, 199--204. |
|
| Strichartz estimates for a Schrödinger operator with nonsmooth coefficients. | with Gigliola Staffilani Comm. Partial Differential Equations 27 (2002), no. 7-8, 1337--1372. |
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| On the Fefferman-Phong inequality and related problems. | Comm. Partial Differential Equations 27 (2002), no. 11-12, 2101--2138 | |
| Nonlinear wave equations. | Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), 209--220 | arXiv:math/0304397 |
| Null form estimates for second order hyperbolic operators with rough coefficients | Harmonic analysis at Mount Holyoke (South Hadley, MA, 2001), 383--409, Contemp. Math., 320 | |
| Phase space transforms and microlocal analysis. | Phase space analysis of partial differential equations. Vol. II, 505--524, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004. | |
| Dispersive estimates for wave equations | with Dan Geba Comm. Partial Differential Equations 30 (2005), no. 4-6, 849--880. |
|
| Sharp local well-posedness results for the nonlinear wave equation. | with Hart Smith Ann. of Math. (2) 162 (2005), no. 1, 291--366. |
dvi-letter, ps-letter |
Sharp Lq |
with Herbert Koch and Hart Smith Math. Res. Lett. 14 (2007), no. 1, 77--85 |
|
| Semiclassical Lp estimates | with Herbert Koch and Maciej
Zworski Ann. Henri Poincaré 8 (2007), no. 5, 885--916 |
arXiv:math-ph/0603080 |
| A phase space transform adapted
to the wave equation |
with Dan Geba Comm. PDE 32 (2007), no. 7-9, 1065--1101. |
|
| Large data local solutions
for the derivative NLS equation |
with Ioan Bejenaru J. Eur. Math. Soc. (JEMS) 10 (2008), no. 4, 957--985 |
arXiv:math/0610092 |
| Wave packet parametrices for
evolutions governed by pdo's with rough symbols |
with Jeremy Marzuola and Jason
Metcalfe Proc. Amer. Math. Soc. 136 (2008), no. 2, 597--604 |
arXiv:math/0611252 |
| Subcritical Lp bounds
on spectral clusters for Lipschitz metrics |
with Herbert Koch and Hart Smith Math. Res. Lett. 14 (2007), no. 1, 77--85. |
arXiv:0709.2764 |
| Gradient NLW on curved
background in 4 + 1 dimensions |
with Dan Geba Int. Math. Res. Not. IMRN 2008, Art. ID rnn 108, 58 pp. |
arXiv:0802.3870 |
| Quasilinear Schroedinger equations I: Small data and quadratic interactions | with Jeremy L. Marzuola and Jason Metcalfe (2011) Adv. Math. 231 (2012), no. 2, 1151-1172. |
arXiv:1106.0490 |
| Sharp L^p bounds on spectral clusters for Lipschitz metrics | with Herbert Koch and Hart Smith (2012) Amer. J. Math. 136 (2014), no. 6, 1629-1663. |
arXiv:1207.2417 |
| Quasilinear Schroedinger equations II: Small data and cubic nonlinearities | with Jeremy Marzuola and Jason Metcalfe (2012) Kyoto J. Math. 54 (2014), no. 3, 529-546. |
arXiv:1208.0544 |
| Quasilinear Schrödinger equations III: Large Data and Short Time | with Jeremy Marzuola and Jason Metcalfe (2020) Arch. Ration. Mech. Anal., 242(2):1119- 1175, 2021. |
arXiv:2001.01014 |
| Local well-posedness for quasilinear problems: a primer | with Mihaela Ifrim (2020) Bull. Amer. Math. Soc. (N.S.), 60(2):167-194, 2023 |
arXiv:2008.05684 |
| The time-like minimal surface equation in Minkowski space: low regularity solutions | with Albert Ai and Mihaela Ifrim (2021) Invent. Math., 235(3):745-891, 2024. |
arXiv:2110.15296 |
| Testing by wave packets and modified scattering in nonlinear dispersive pde's | with Mihaela Ifrim (2020) Trans. Amer. Math. Soc. Ser. B, 11:164-214, 2024. |
arXiv:arXiv:2204.13285 |
Wave Maps
| Local and global results for wave maps. I | Comm. Partial Differential Equations 23 (1998), no. 9-10, 1781--1793 | |
| On global existence and scattering for the wave maps equation | Amer. J. Math. 123 (2001), no. 3, 385--423. | pdf |
| The wave maps equation | Bull. Amer. Math. Soc. (N.S.) 41 (2004), no. 2, 185--204 | pdf Journal |
| Rough solutions for the wave maps equation | Amer. J. Math. 127 (2005), no. 2, 293--377. | |
| Energy dispersed large data wave maps in 2+1 dimensions | with Jacob Sterbenz Comm. Math. Phys. 298 (2010), no. 1, 139-230 |
arXiv:0810.5766 |
| Regularity of Wave-Maps in dimension 2+1 | with Jacob Sterbenz Comm. Math. Phys. 298 (2010), no. 1, 231-264 |
arXiv:0907.3148 |
| Wave maps on (1+2)-dimensional curved spacetimes | with Cristian Gavrus and Casey Jao Anal. PDE, 14(4):985-1084, 2021 |
arXiv:1810.05632 |
Schroedinger Maps.
| Global Schrödinger maps in dimension two and higher: small data in the critical Sobolev spaces | with Ioan Bejenaru, Alexandru Ionescu and Carlos Kenig (2008) Ann. of Math. (2) 173 (2011), no. 3, 1443-1506 |
arXiv:0807.0265v1 |
| Equivariant Schroedinger Maps in two spatial dimensions | with Ioan Bejenaru, Alexandru Ionescu and Carlos Kenig (2011) Duke Math. J. 162 (2013), no. 11 |
arXiv:1112.6122 |
| Equivariant Schroedinger Maps in two spatial dimensions: the H^2 target | with Ioan Bejenaru, Alexandru Ionescu and Carlos Kenig (2012) Kyoto J. Math. 56 (2016), no. 2, 283-323. |
arXiv:1212.2566 |
Near soliton evolutions in geometric dispersive flows.
| Renormalization and blow up for
charge one equivariant critical wave maps |
with Joachim Krieger and Wilhelm
Schlag Invent. Math. 171 (2008), no. 3, 543--615. |
arXiv:math/0610248 |
| Slow blow-up solutions for the H1(R3)
critical focusing semi-linear wave equation |
with Joachim Krieger and Wilhelm
Schlag Duke Math. J. 147 (2009), no. 1, 1--53. |
arXiv:math/0702033 |
| Renormalization and blow up for the critical Yang-Mills problem. | with Joachim Krieger and Wilhelm Schlag Adv. Math. 221 (2009), no. 5, 1445--1521 |
arXiv:0809.2114 |
| Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions | with Ioan Bejenaru (2010) Mem. Amer. Math. Soc. 228 (2010), no. 1069 |
arXiv:1009.1608 |
| A codimension two stable manifold of near soliton equivariant wave maps | with Ioan Bejenaru and Joachim Krieger (2011) Anal. PDE 6 (2013), no. 4, 829-857. |
arXiv:1109.3129 |
Decay of linear waves on asymptotically flat space times. Some of this is GR based/motivated.
| Parametrices and dispersive
estimates for Schrödinger operators with variable coefficients |
Amer. J. Math. 130 (2008), no. 3, 571--634. |
|
| Local decay of waves on asymptotically flat stationary space-times | (2009) Amer. J. Math. 135 (2013), no. 2, 361-401. |
arXiv:0910.5290 |
| Strichartz estimates and local
smoothing estimates for asymptotically flat Schrödinger equations |
with Jeremy Marzuola and Jason
Metcalfe J. Funct. Anal. 255 (2008), no. 6, 1497--1553. |
arXiv:0706.0544 |
| Global parametrices and
dispersive estimates for variable coefficients wave equations |
with Jason Metcalfe Math. Ann. 353 (2012), no. 4, 1183-1237 |
arXiv:0707.1191 |
| Decay estimates for variable coefficient wave equations in exterior domains | with Jason Metcalfe Advances in phase space analysis of partial differential equations, 201-216, Progr. Nonlinear Differential Equations Appl., 78 |
arXiv:0806.3409 | Strichartz
estimates on Schwarzschild black hole backgrounds |
with Jeremy Marzuola, Jason
Metcalfe
and Mihai Tohaneanu Comm. Math. Phys. 293 (2010), no. 1, 37--83. |
arXiv:0802.3942 |
| A local energy estimate on Kerr black hole backgrounds | with Mihai Tohaneanu (2008) IMRN 2011, no. 2, 248-292 |
arXiv:0810.5766 |
| Price's Law on Nonstationary Spacetimes | with Jason Metcalfe and Mihai Tohaneanu (2011) Adv. Math. 230 (2012), no. 3, 995-1028. |
arXiv:1104.5437 |
| Local energy decay for Maxwell fields part I: Spherically symmetric black-hole backgrounds | with Jacob Sterbenz (2013) Int. Math. Res. Not. IMRN 2015, no. 11, 3298-3342. |
arXiv:1305.5261 |
| Pointwise decay for the Maxwell field on black hole space-times |
with Jason Metcalfe and Mihai Tohaneanu
(2014) Adv. Math. 316 (2017), 53-93. |
arXiv:1411.3693 |
| Local energy decay for scalar fields on time dependent non-trapping backgrounds |
with Jason Metcalfe, Jacob Sterbenz
(2017) Amer. J. Math., 142(3):821-883, 2020 |
arXiv:1703.08064 |
Geometric nonlinear waves. Primarily MKG and YM.
| Global well-posedness for the Maxwell-Klein Gordon equation in 4+1 dimensions. Small energy | with Joachim Krieger and Jacob Sterbenz (2012) Duke Math. J. 164 (2015), no. 6, 973-1040. |
arXiv:1211.3527 |
| Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity |
with Sung-Jin Oh
(2015) Ann. PDE 2 (2016), no. 1, Art. 2, 70 |
arXiv:1503.01560 |
| Energy dispersed solutions for the (4+1)-dimensional Maxwell-Klein-Gordon equation |
with Sung-Jin Oh
(2015) Amer. J. Math., 140(1):1-82, 2018 |
arXiv:1503.01561 |
| Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation |
with Sung-Jin Oh
(2015) Invent. Math. 205 (2016), no. 3, 781-877. |
arXiv:1503.01562 |
| Global well-posedness for the Yang-Mills equation in 4+1 dimensions. Small energy |
with Joachim Krieger
(2015) Ann. of Math. (2) 185 (2017), no. 3, 831-893 |
arXiv:1509.00751 |
| The Yang--Mills heat flow and the caloric gauge |
with Sung-Jin Oh
(2017) Ast ́erisque, (436):viii+128, 2022 |
arXiv:1709.08599 |
| The hyperbolic Yang--Mills equation in the caloric gauge. Local well-posedness and control of energy dispersed solutions |
with Sung-Jin Oh
(2017) Pure Appl. Anal., 2(2):233–384, 2020 |
arXiv:1709.09332 |
| The hyperbolic Yang--Mills equation for connections in an arbitrary topological class |
with Sung-Jin Oh
(2017) Comm. Math. Phys., 365(2):685-739, 2019 |
arXiv:1709.08604 |
| The threshold conjecture for the energy critical hyperbolic Yang--Mills equation |
with Sung-Jin Oh
(2017) Ann. of Math. (2), 194(2):393-473, 2021 |
arXiv:1709.08606 |
| The Threshold Theorem for the (4+1)-dimensional Yang--Mills equation: an overview of the proof |
with Sung-Jin Oh
(2017) Bull. Amer. Math. Soc. (N.S.), 56(2):171-210, 2019 |
arXiv:1709.09088 |
Fluid dynamics. This also includes model problems arising in the study of various fluid models.
| Well-posedness for the Navier-Stokes equations. | with Herbert Koch Adv. Math. 157 (2001), no. 1, 22--35. |
|
| Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method | with John K. Hunter, Mihaela Ifrim and Tak Kwong Wong (2013) Proc. Amer. Math. Soc. 143 (2015), no. 8, 3407-3412. |
arXiv:1301.1947 |
| Two dimensional water waves in holomorphic coordinates | with John K. Hunter and Mihaela Ifrim (2013) Comm. Math. Phys. 346 (2016), no. 2, 483-552. |
arXiv:1401.1252 |
| Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension | with Mihaela Ifrim (2014) Nonlinearity 28 (2015), no. 8, 2661-2675. |
arXiv:1404.7581 |
| Two dimensional water waves in holomorphic coordinates II: global solutions |
with Mihaela Ifrim
(2014) Bull. Soc. Math. France 144 (2016), no. 2, 369-394. |
arXiv:1404.7583 |
| The lifespan of small data solutions in two dimensional capillary water waves |
with Mihaela Ifrim
(2014) Arch. Ration. Mech. Anal. 225 (2017), no. 3, 1279-1346. |
arXiv:1406.5471 |
| The lifespan of small data solutions to the KP-I |
with Benjamin Harrop-Griffiths and Mihaela Ifrim
(2014) Int. Math. Res. Not. IMRN 2017, no. 1, 1-28. |
arXiv:1409.4487 |
| Two dimensional gravity water waves with constant vorticity: I. Cubic lifespan |
with Mihaela Ifrim
(2015) Anal. PDE, 12(4):903–967, 2019 |
arXiv:1510.07732 |
| Finite depth gravity water waves in holomorphic coordinates |
with Mihaela Ifrim
(2016) Ann. PDE 3 (2017), no. 1, Art. 4, 102 pp. |
arXiv:1607.02409 |
| Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation |
with Mihaela Ifrim
(2017) Ann. Sci. ́Ec. Norm. Sup ́er. (4), 52(2):297- 335, 2019 |
arXiv:1701.08476 |
| A Morawetz inequality for water waves | with Thomas Alazard and Mihaela Ifrim (2018) Amer. J. Math., 144(3):607-699, 2022 |
arXiv:1806.08443 |
| No solitary waves in 2D gravity and capillary waves in deep water | with Mihaela Ifrim (2018) Nonlinearity, 33(10):5457-5476, 2020 |
arXiv:1808.07916 |
| The NLS approximation for two dimensional deep gravity waves | with Mihaela Ifrim (2018) Sci. China Math., 62(6):1101–1120, 2019. |
arXiv:1809.05060 |
| Dispersive decay of small data solutions for the KdV equation | with Mihaela Ifrim and Herbert Koch (2019) Ann. Sci. ́Ec. Norm. Sup ́er. (4), 56(6):1709-1746, 2023 |
arXiv:1901.05934 |
| A Morawetz inequality for gravity-capillary water waves at low Bond number | with Thomas Alazard and Mihaela Ifrim (2019) Water Waves, 3(3):429-472, 2021. |
arXiv:1910.02529 |
| Two dimensional gravity waves at low regularity I: Energy estimates | with Albert Ai and Mihaela Ifrim (2019) preprint |
arXiv:1910.05323 |
| Two dimensional gravity waves at low regularity II: Global solutions | with Albert Ai and Mihaela Ifrim (2019) Ann. Inst. H. Poincare C Anal. Non Lineaire, 39(4):819- 884, 2022. |
arXiv:2009.11513 |
| No pure capillary solitary waves exist in 2D finite depth | with Mihaela Ifrim, Ben Pineau and Mitchell Taylor (2021) SIAM J. Math. Anal., 54(4):4452-4464, 2022. |
arXiv:2104.07845 |
| The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity | with Mihaela Ifrim, James Rowan and Lizhe Wan (2021) Ars Inven. Anal., pages Paper No. 3, 33, 2022. |
arXiv:2108.08964 |
Integrable models and inverse scattering.
This portion only includes work on integrable models which involves inverse scattering
in one way or another. However, integrable models occur also as
part of the other projects, in particular as water wave models in
fluids.
| Conserved energies for the cubic NLS in 1-d |
with Herbert Koch
(2016) Duke Math. J., 167(17):3207-3313, 2018. |
arXiv:1607.02534 |
| A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davewy-Stewartson Equation and to the Inverse Boundary Value Problem of Calderon |
with Adrian I. Nachman, Idan Regev
(2017) Invent. Math., 220(2):395-451, 2020. |
arXiv:1708.04759 |
| Multisolitons for the cubic NLS in 1-d and their stability | with Herbert Koch (2012) Publications Math ́ematiques de l'IHES, to appear. |
arXiv:2008.13352 |
Free boundary problems.
This work is primarily about free boundary problems arising in fluid dynamics, either of
the compressible or incompressible variety.
| The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach | with Mihaela Ifrim (2020) Ann. Inst. H. Poincar ́e C Anal. Non Lin ́eaire, 41(2):405-495, 2024. |
arXiv:2007.05668 |
| The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion | with Marcelo Disconzi and Mihaela Ifrim (2020) Arch. Ration. Mech. Anal., 245(1):127-182, 2022. |
arXiv:2007.05787 |
| Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations | with Mihaela Ifrim, Ben Pineau and Mitchell Taylor (2023) preprint |
arXiv:2309.05625 |
Skew Mean Curvature Flow.
This is the Schroedinger counterpart of the mean curvature flow, for codimension two embedded submanifolds.
| Local well-posedness of skew mean curvature flow for small data in d≥4 dimensions | with Jiaxi Huang (2021) Comm. Math. Phys., 389(3):1569-1645, 2022. |
arXiv:2101.00358 |
| Local well-posedness of the Skew mean curvature flow for small data in d≥2 dimensions | with Jiaxi Huang (2022) Arch. Ration. Mech. Anal., 248(1):10, 2024. |
arXiv:2202.10632 |
| Global regularity of Skew mean curvature flow for small data in d≥4 dimensions | with Jiaxi Huang and Ze Li (2022) nt. Math. Res. Not. IMRN, (5):3748-3798, 2024 |
arXiv:2209.08941 |
The global well-posedness conjectures.
These conjectures are concerned with global well-posedness for dispersive pde's in strongly nonlinear regimes
| Global solutions for 1D cubic defocusing dispersive equations: Part I | with Mihaela Ifrim (2022) Forum Math. Pi, 11:Paper No. e31, 46, 2023. |
arXiv:2205.12212 |
| Long time solutions for 1D cubic dispersive equations, Part II: the focusing case | with Mihaela Ifrim (2022) Vietnam Journal of Mathematics, Special issue dedicated to Carlos Kenig, to appear |
arXiv:2210.17007 |
| Global solutions for 1D cubic dispersive equations, Part III: the quasilinear Schrödinger flow | with Mihaela Ifrim (2022) preprint. |
arXiv:2306.00570 |
| The global well-posedness conjecture for 1D cubic dispersive equations | with Mihaela Ifrim (2023) preprint |
arXiv:2311.15076 |
| Global solutions for cubic quasilinear Schroedinger flows in two and higher dimensions | with Mihaela Ifrim (2024) preprint |
arXiv:2404.09970 |