249 citations · 684 across the 32 of their papers we have counts for
46 papers · 1 filter
Generic small-scale creation in the two-dimensional Euler equation
Thomas Alazard, Ayman Rimah Said
The Cauchy problem for the two-dimensional incompressible Euler equation is globally well-posed for smooth initial data. In this paper, we show that for a dense set of initia…
Global well-posedness of a 2D fluid-structure interaction problem with free surface
Thomas Alazard, Chengyang Shao, Haocheng Yang
This paper is devoted to the analysis of the incompressible Euler equation in a time-dependent fluid domain, whose interface evolution is governed by the law of linear elasticity.…
Nonlinear interpolation and the flow map for quasilinear equations
Thomas Alazard, Nicolas Burq, Mihaela Ifrim +2
We prove an interpolation theorem for nonlinear functionals defined on scales of Banach spaces that generalize Besov spaces. It applies to functionals defined only locally, requiri…
Paracomposition Operators and Paradifferential Reducibility
Thomas Alazard, Chengyang Shao
Reducibility methods, aiming to simplify systems by conjugating them to those with constant coefficients, are crucial for studying the existence of quasiperiodic solutions. In KAM…
Global-in-time weak solutions for an inviscid free surface fluid-structure problem without damping
Thomas Alazard, Igor Kukavica, Amjad Tuffaha
We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-…
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…