Small-amplitude, traveling, space periodic solutions–called Stokes waves–of the 2
dimensional gravity water waves equations in deep water are linearly unstable with respect …

We prove the existence of small amplitude time quasi‐periodic solutions of the pure gravity
water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom …

We prove the existence of steady space quasi-periodic stream functions, solutions for the
Euler equation in a vorticity-stream function formulation in the two dimensional channel R× …

The paper fully answers a long standing open question concerning the stability/instability of
pure gravity periodic traveling water waves—called Stokes waves—at the critical Whitham …

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 the existence of time quasi-periodic vortex patch solutions of the 2 d-Euler
equations in R 2, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios …

In this paper we paralinearize the contour dynamics equation for sharp-fronts of α-SQG, for
any α∈(0, 1)∪(1, 2), close to a circular vortex. This turns out to be a quasi-linear …

Whitham and Benjamin predicted in 1967 that small-amplitude periodic traveling Stokes
waves of the 2d-gravity water waves equations are linearly unstable with respect to long …

In this paper, we investigate the inviscid limit ν→ 0 for time-quasi-periodic solutions of the
incompressible Navier–Stokes equations on the two-dimensional torus T 2, with a small time …

We prove the existence of large amplitude bi-periodic traveling waves (stationary in a
moving frame) of the two-dimensional non-resistive Magnetohydrodynamics (MHD) system …