4 papers
Local Invariant Structures in the Dynamics of Capillary Water Jet
Chengyang Shao, Haocheng Yang
Physical experiments show that a capillary water jet is exponentially unstable under long wave perturbations, while remaining stable under short wave perturbations. Measurements in…
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…