In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler
equations describing the motion of a liquid in an unbounded initial domain with moving …

The well-known Stokes waves refer to periodic traveling waves under the gravity at the free
surface of a two dimensional full water wave system. In this paper, we prove that small …

In this paper, by considering 2d water waves with a pair of point vortices, we prove the
existence of water waves with sign-changing Taylor sign coefficients. That is, the strong …

In this paper, we study the motion of the two dimensional inviscid incompressible, infinite
depth water waves with point vortices in the fluid. We show that the Taylor sign condition-∂ …

We consider the Cauchy problem for the full free boundary Euler equations in $3 $ d with an
initial small velocity of size $ O (\epsilon_0) $, in a moving domain which is initially an $ O …

In this paper we prove the existence of water waves with sign-changing Taylor sign
coefficients, that is, the strong Taylor sign holds initially, while breaks down at a later time …

The Euler–Korteweg system is a dispersive perturbation of the usual compressible Euler
equations. In dimension at least three, under a natural stability condition on the pressure, the …

Ce manuscrit décrit quelques résultats d'analyse des équations aux dérivées partielles qui
ont pour fil rouge l'équation de Schrödinger non linéaire. Les chapitres 1 et 2 sont dédiés à …