We consider the gravity water waves system in the case of a one dimensional interface, for
sufficiently smooth and localized initial data, and prove global existence of small solutions …

We are interested in the system of gravity water waves equations without surface tension.
Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of …

La démonstration est basée sur un argument inductif faisant intervenir des estimations a
priori dans L2 et L∞. Les bornes L2 sont prouvées dans [5], texte complémentaire au …

We review recent progress on the long-time regularity of solutions of the Cauchy problem for
the water waves equations, in two and three dimensions. We begin by introducing the free …

In this paper we prove global regularity for the full water-wave system in three dimensions
for small data, under the influence of both gravity and surface tension. This problem presents …

We study the dynamics of the interface between two incompressible fluids in a two-
dimensional porous medium whose flow is modeled by the Muskat equations. For the two …

We consider the full irrotational water waves system with surface tension and no gravity in
dimension two (the capillary waves system), and prove global regularity and modified …

We prove an almost global existence result for space periodic solutions of the 1D gravity-
capillary water waves equations with constant vorticity. The result holds for any value of …

We prove that the three dimensional stable Muskat problem is globally well-posed in the
critical Sobolev space H˙ 2∩ W˙ 1,∞ provided that the semi-norm‖ f 0‖ H˙ 2 is small …

In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat
problem, we rule out the “splash singularity” blow-up scenario; in other words, we prove that …