School of Mathematics and Statistics
Guangdong University of Technology
Guangzhou, 510520, China
email: pingxiaozhai@163.com
Xiaoping Zhai
Abstract:
In this article, we study the linear stability of a two-dimensional non-isentropic
compressible fluid with vanishing shear viscosity in the context of Couette flow on an
infinitely long flat torus \(\mathbb{T} \times \mathbb{R}\).
By employing explicit weighted energy estimates and the Fourier multipliers method,
we first establish the inviscid damping of the incompressible component of the velocity.
Subsequently, we derive an upper bound which is superlinear in time for the compressible
part of the fluid. Furthermore, we demonstrate an enhanced dissipation phenomenon for
the velocity field under certain quality conditions pertaining to the initial density,
initial temperature, and incompressible component of the initial velocity field.
Submitted May 23, 2025. Published November 14, 2025.
Math Subject Classifications: 76E05, 76E19.
Key Words: Stability; compressible Navier-Stokes equations; Couette flow; enhanced dissipation
DOI: 10.58997/ejde.2025.107
Show me the PDF file (356 KB), TEX file for this article.
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Xiaoping Zhai School of Mathematics and Statistics Guangdong University of Technology Guangzhou, 510520, China email: pingxiaozhai@163.com |
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