5 papers · 1 filter
Cheeger's Constant for the Gabor Transform and Ripples
Rima Alaifari, Ben Pineau, Mitchell A. Taylor +1
We discover a new instability mechanism for short-time Fourier transform phase retrieval which yields that for any reasonable window function in any dimension , the local s…
On the optimal Sobolev threshold for evolution equations with rough nonlinearities
Ben Pineau, Mitchell A. Taylor
In this article we are concerned with evolution equations of the form \begin{equation*} \partial_tu-A(D)u=F(u,\overline{u},\nabla u, \nabla \overline{u}) \end{equation*} where $A(D…
Global well-posedness for the generalized derivative nonlinear Schrödinger equation
Ben Pineau, Mitchell A. Taylor
We study the well-posedness of the generalized derivative nonlinear Schrödinger equation (gDNLS) for small powers . We analyze this equation at…
Global solutions for cubic quasilinear ultrahyperbolic Schrödinger flows
Mihaela Ifrim, Ben Pineau, Daniel Tataru
In recent work, two of the authors proposed a broad global well-posedness conjecture for cubic quasilinear dispersive equations in two space dimensions, which asserts that global w…
Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations
Mihaela Ifrim, Ben Pineau, Daniel Tataru +1
We provide a complete local well-posedness theory in based Sobolev spaces for the free boundary incompressible Euler equations with zero surface tension on a connected fluid…