6 papers
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 initi…
The Hele-Shaw semi-flow
Thomas Alazard, Herbert Koch
We prove that the Cauchy problem is well-posed in a strong sense and in a general setting. Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem wi…
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 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.…
KAM via Standard Fixed Point Theorems
Thomas Alazard, Chengyang Shao
With a mere usage of well-established properties of para-differential operators, the conjugacy equations in several model KAM problems are converted to para-homological equations s…
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…