Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations
Qi Chen
Zhejiang University, Hangzhou, P. R. ChinaDongyi Wei
Peking University, Beijing, P. R. ChinaPing Zhang
Chinese Academy of Sciences, Beijing, P. R. ChinaZhifei Zhang
Peking University, Beijing, P. R. China

Abstract
We prove the asymptotic stability of shear flows close to the Couette flow for the 2-D inhomogeneous incompressible Euler equations on . More precisely, if the initial velocity is close to the Couette flow and the initial density is close to a positive constant in the Gevrey class 2, then 2-D inhomogeneous incompressible Euler equations are globally well-posed and the velocity converges strongly to a shear flow close to the Couette flow, and the vorticity will be driven to small scales by a linear evolution and weakly converges as . To our knowledge, this is the first global well-posedness result for the 2-D inhomogeneous incompressible Euler equations.
Cite this article
Qi Chen, Dongyi Wei, Ping Zhang, Zhifei Zhang, Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations. J. Eur. Math. Soc. (2025), published online first
DOI 10.4171/JEMS/1608