58 citations · 61 across the 6 of their papers we have counts for
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Paralinearization of free boundary problems in fluid dynamics
Thomas Alazard
A classical topic in the mathematical theory of hydrodynamics is to study the evolution of the free surface separating air from an incompressible perfect fluid. The goal of this su…
Damping for fractional wave equations and applications to water waves
Thomas Alazard, Jeremy L. Marzuola, Jian Wang
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for suff…
Virial theorems and equipartition of energy for water-waves
Thomas Alazard, Claude Zuily
We study several different aspects of the energy equipartition principle for water waves. We prove a virial identity that implies that the potential energy is equal, on average, to…
Stabilization of the water-wave equations with surface tension
Thomas Alazard
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved…
Gravity capillary standing water waves
Thomas Alazard, Pietro Baldi
The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its…
Strichartz estimates and the Cauchy problem for the gravity water waves equations
Thomas Alazard, Nicolas Burq, Claude Zuily
This paper is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the init…