| Department
of
Mathematics University of California, Berkeley Berkeley, CA 94720, USA |
Office: Evans Hall 841
Phone: (510) 643-1284
Email: tataru@math.berkeley.edu
|
Address:
Office: Evans Hall 841
|
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.
Following are some selected published papers, as well as all the new
preprints.
| Local and global results for wave maps. I | Comm. Partial Differential Equations 23 (1998), no. 9-10, 1781--1793 | |
| 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. |
|
| Unique continuation for operators with partially analytic coefficients | J. Math. Pures Appl. (9) 78 (1999), no. 5, 505--521. | |
| On the equation u=| ∇ u|2 in 5+1 dimensions. | Math. Res. Lett. 6 (1999), no. 5-6, 469--485 | |
| Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation | Amer. J. Math. 122 (2000), no. 2, 349--376 | |
| 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 |
| Sharp counterexamples in unique continuation for second order elliptic equations | with Herbert Koch J. Reine Angew. Math. 542 (2002), 133--146. |
pdf |
| Well-posedness for the Navier-Stokes equations. | with Herbert Koch Adv. Math. 157 (2001), no. 1, 22--35. |
|
| 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 |
| On global existence and scattering for the wave maps equation | Amer. J. Math. 123 (2001), no. 3, 385--423. | pdf |
| 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. |
|
| 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. | |
| The wave maps equation | Bull. Amer. Math. Soc. (N.S.) 41 (2004), no. 2, 185--204 | pdf Journal |
| Dispersive estimates for principally normal pseudodifferential operators. | Comm. Pure Appl. Math. 58 (2005), no. 2, 217--284. | arXiv:math/0401234 |
| Rough solutions for the wave maps equation | Amer. J. Math. 127 (2005), no. 2, 293--377. | |
| Lp eigenfunction bounds for the Hermite operator. | with Herbert Koch Duke Math. J. 128 (2005), no. 2, 369--392. |
arXiv:math/0402261 |
| 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 |
| Carleman estimates and absence of embedded eigenvalues. | with Herbert Koch Comm. Math. Phys. 267 (2006), no. 2, 419--449. |
arXiv:math-ph/0508052 |
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. |
|
| Parametrices and dispersive
estimates for Schrödinger operators with variable coefficients |
Amer. J. Math. 130 (2008), no. 3, 571--634. |
|
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 to appear, Mathematische Annalen |
arXiv:0707.1191 |
| 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 |
| 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 |
| Global Schrödinger maps in dimension two and higher: small data in the critical Sobolev spaces | with Ioan Bejenaru, Alexandru Ionescu and Carlos Kenig (2008) preprint, to appear in Annals of Math. |
arXiv:0807.0265v1 |
| 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 |
| 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 |
| 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 |
| 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 |
| A local energy estimate on Kerr black hole backgrounds | with Mihai Tohaneanu (2008) IMRN 2011, no. 2, 248–292 |
arXiv:0810.5766 |
| 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 |
| Local decay of waves on asymptotically flat stationary space-times | (2009) to appear, AJM |
arXiv:0910.5290 |
| 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) to appear in Duke Math. J. |
arXiv:1005.2832 |
| Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions | with Ioan Bejenaru (2010) preprint |
arXiv:1009.1608 |
| Strichartz estimates for partially periodic solutions to Schroedinger equations in 4d and applications | with Sebastian Herr, Nikolay Tzvetkov (2010) preprint |
arXiv:1011.0591 |
| Energy and local energy bounds for the 1-D cubic NLS equation in H^{-1/4} | with Herbert Koch (2010) to appear, Math. Ann. |
arXiv:1012.0148 |
| Price's Law on Nonstationary Spacetimes | with Jason Metcalfe and Mihai Tohaneanu (2011) preprint |
arXiv:1104.5437 |
| Quasilinear Schrödinger equations I: Small data and quadratic interactions | with Jeremy L. Marzuola and Jason Metcalfe (2011) preprint |
arXiv:1106.0490 |
| Uniqueness in Calderon's problem with Lipschitz conductivities | with Boaz Haberman (2011) preprint |
arXiv:1108.6068 |
| A codimension two stable manifold of near soliton equivariant wave maps | with Ioan Bejenaru and Joachim Krieger (2011) preprint |
arXiv:1109.3129 |