249 citations · 684 across the 32 of their papers we have counts for
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math.AP2019
A Morawetz inequality for gravity-capillary water waves at low Bond number
Thomas Alazard, Mihaela Ifrim, Daniel Tataru
This paper is devoted to the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the general question of proving Morawetz inequalities. We conti…
math.AP2019★ 41 cited
Paralinearization of the Muskat equation and application to the Cauchy problem
Thomas Alazard, Omar Lazar
We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-pose…
math.AP2019★ 20 cited
Lyapunov functions, Identities and the Cauchy problem for the Hele-Shaw equation
Thomas Alazard, Nicolas Meunier, Didier Smets
This article is devoted to the study of the Hele-Shaw equation. We introduce an approach inspired by the water-wave theory. Starting from a reduction to the boundary, introducing t…