Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations

  • Qi Chen

    Zhejiang University, Hangzhou, P. R. China
  • Dongyi Wei

    Peking University, Beijing, P. R. China
  • Ping Zhang

    Chinese Academy of Sciences, Beijing, P. R. China
  • Zhifei Zhang

    Peking University, Beijing, P. R. China
Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations cover
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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