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arXiv · 2303.14858

Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations

Qi Chen·Dongyi Wei·Ping Zhang·Zhifei Zhang
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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 $\mathbb{T}\times \mathbb{R}$. 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 $t\to \infty$. To our knowledge, this is the first global well-posedness result for the 2-D inhomogeneous incompressible Euler equations.

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Qi Chen, Dongyi Wei, Ping Zhang, Zhifei Zhang. 2023-03-27. Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations. https://arxiv.org/abs/2303.14858

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