Ben Pineau

I'm a fifth-year PhD student in the mathematics department at UC Berkeley. My main area of study is in nonlinear partial differential equations. I'm particularly interested in physically motivated models, some of which include Schrödinger equations, free boundary Euler equations, water waves, and the equations of magnetohydrodynamics. I am also interested in stable phase retrieval.

My advisor is Daniel Tataru

Papers and preprints

A sharp upper bound on the range of Sobolev exponents for which the NLS and NLW equations admit solutions, joint with Mitchell Taylor, in preparation.
Low regularity solutions for the general quasilinear ultrahyperbolic Schrödinger equation, joint with Mitchell Taylor. arXiv:2310.19221 [math.AP]
Sharp Hadamard local well-posedness, enhanced uniqueness, and pointwise continuation criterion for the incompressible free boundary Euler equations, joint with Mihaela Ifrim, Daniel Tataru, and Mitchell Taylor. arXiv:2309.05625 [math.AP]
Stable phase retrieval in function spaces, joint with Daniel Freeman, Timur Oikhberg, and Mitchell Taylor, accepted in Math. Ann. arXiv:2210.05114 [math.FA]
Examples of Hölder-Stable Phase Retrieval, joint with Michael Christ and Mitchell Taylor, accepted in Math. Res. Lett. arXiv:2205.00187 [math.CA]
Global well-posedness for the generalized derivative nonlinear Schrödinger equation, joint with Mitchell Taylor. arXiv:2112.04648 [math.AP]
No pure capillary solitary waves exist in 2D finite depth, joint with Mihaela Ifrim, Daniel Tataru and Mitchell Taylor, accepted in SIAM J. Math. Anal. arXiv:2104.07845 [math.AP]
New Regularity Criteria for the Navier-Stokes Equations in Terms of Pressure, joint with Xinwei Yu. arXiv:1910.08911 [math.AP]
On Prodi–Serrin type conditions for the 3D Navier–Stokes equations, joint with Xinwei Yu, Nonlinear Analysis Theory Methods and Applications. Vol. 190, (2020). link
A New Prodi–Serrin Type Regularity Criterion in Velocity Directions, joint with Xinwei Yu, Journal of Mathematical Fluid Mechanics. Vol. 20, pages 1737–1744 (2018). link

Seminar and conference participation

Invited speaker at conference on lattice problems in analysis. May, 2024 (Tentatively). ICMAT, Madrid, Spain.
UCLA Analysis and PDE seminar. November 28th, 2023. UCLA, Los Angeles, CA, USA.
Oberwolfach seminar: Scattering Resonances in Quantum Mechanics, General Relativity and Hyperbolic Dynamics . November, 2023. Oberwolfach, Germany.

ETH Zurich Analysis seminar. Nov. 14th, 2023. ETH, Zurich, Switzerland.

UC Berkeley Analysis and PDE seminar. Sept. 25th, 2023. UC Berkeley, Berkeley, CA, USA.

MSRI, FD2 Reunion seminar. August 10th, 2023. Simons Laufer Mathematical Sciences Institute, Berkeley, CA, USA.

Wisconsin PDE seminar. April. 24th, 2023. University of Wisconsin–Madison, Madison, WI, USA.

ICMAT PDE’s and Fluid Mechanics seminar. Nov. 3rd, 2022. ICMAT, Madrid, Spain.

Oberwolfach seminar: Free Boundary Problems in Fluid Dynamics . October, 2022. Oberwolfach, Germany.

Harmonic Analysis and Differential Equations Seminar (HADES). May 10th, 2022. UC Berkeley, Berkeley, CA, USA.

PDE Learning Seminar (Fall 2021) Nonlinear wave equations and general relativity. Nov. 3rd, 2021; via Zoom. UC Berkeley, Berkeley, CA, USA.

Harmonic Analysis and Differential Equations Seminar (HADES). Oct. 26th, 2021. UC Berkeley, Berkeley, CA, USA.

MSRI, Mathematical problems in fluid dynamics graduate student working group. May. 12th, 2021; via Zoom. MSRI, CA, USA.

Seminar on wave packets in dispersive PDE. Nov. 17th, 2020; via Zoom. UC Berkeley, Berkeley, CA, USA.

Seminar on singularity formation for incompressible Euler. Mar, 2020. UC Berkeley, Berkeley, CA, USA.

Harmonic Analysis and Differential Equations Seminar (HADES). Nov. 19th, 2019. UC Berkeley, Berkeley, CA, USA.

The XI Americas Conference on Differential Equations and Nonlinear Analysis. August 19, 2017, University of Alberta, Edmonton, Canada.

Teaching and seminar organization
In Fall 2023, I am a GSR. My office is at Evans 1049. I am also co-organizing the Harmonic Analysis and Differential Equations Seminar (HADES) with Ovidiu Avadanei, Izak Oltman and Ely Sandine.