Strichartz estimates for gravity water waves

Abstract

We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled in $L^{\infty }$-norm, or the initial free surface has a curvature not controlled in $L^2$-norm.

59 pages. This paper relies, for some parts, on our previous article arXiv:1212.0626

References in corpus (5)

• On the Water Waves Equations with Surface Tension
• Boundary estimates for positive solutions to second order elliptic equations
• Overview of the proof of the Bounded $L^2$ Curvature Conjecture
• Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations
• Break-down criterion for the water-wave equation