5 papers · 1 filter
Global solutions for cubic quasilinear Schroedinger flows in two and higher dimensions
Mihaela Ifrim, Daniel Tataru
In recent work the authors proposed a broad global well-posedness conjecture for cubic defocusing dispersive equations in one space dimension, and then proved this conjecture in tw…
Global solutions for 1D cubic dispersive equations, Part III: the quasilinear Schrödinger flow
Mihaela Ifrim, Daniel Tataru
The first target of this article is the local well-posedness question for 1D quasilinear Schrödinger equations with cubic nonlinearities. The study of this class of problems, in a…
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…
Global solutions for 1D cubic defocusing dispersive equations, Part IV: general dispersion relations
Mihaela Ifrim, Daniel Tataru
A broad conjecture, formulated by the authors in earlier work, reads as follows: "Cubic defocusing dispersive one dimensional flows with small initial data have global dispersive s…
Nonlinear interpolation and the flow map for quasilinear equations
Thomas Alazard, Nicolas Burq, Mihaela Ifrim +2
We prove an interpolation theorem for nonlinear functionals defined on scales of Banach spaces that generalize Besov spaces. It applies to functionals defined only locally, requiri…