4 papers · 1 filter
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…
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…
Low regularity solutions for the general quasilinear ultrahyperbolic Schrödinger equation
Ben Pineau, Mitchell A. Taylor
We present a novel method for establishing large data local well-posedness in low regularity Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and n…
Sharp well-posedness for the free boundary MHD equations
Mihaela Ifrim, Ben Pineau, Daniel Tataru +1
In this article, we provide a definitive well-posedness theory for the free boundary problem in incompressible magnetohyrodynamics. Despite the clear physical interest in this syst…