Ben Pineau

I'm a fourth year PhD student in the mathematics department at UC Berkeley. My main area of study is in nonlilnear 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 phase retrieval.

My advisor is Daniel Tataru

Papers and preprints

Stable phase retrieval in function spaces, joint with Daniel Freeman, Timur Oikhberg and Mitchell Taylor. arXiv:2210.05114 [math.FA]
Examples of Hölder-Stable Phase Retrieval, joint with Michael Christ and Mitchell Taylor. 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, to appear in SIAM Journal on Mathematical Analysis. 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 talks

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

In Fall 2022, I am a GSR. My office is at Evans 1075. For this semester, I'm typically in on Monday and Tuesday afternoons and occasionally other days if you need to reach me.