Linear stability of the Couette flow in the 3D isentropic compressible Navier-Stokes equations

Lan Zeng; Zhifei Zhang; Ruizhao Zi

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arXiv · 2105.10200

Linear stability of the Couette flow in the 3D isentropic compressible Navier-Stokes equations

Lan Zeng·Zhifei Zhang·Ruizhao Zi

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Abstract

Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible Navier-Stokes equations around the Couette flow $(y, 0, 0)^\top$. Moreover, the lift-up phenomenon is also shown in this paper. Compared with the 3D incompressible Navier-Stokes equations [Ann. of Math.,185(2017), 541--608], the lift-up effect here is stronger due to the loss of the incompressible condition.

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Lan Zeng, Zhifei Zhang, Ruizhao Zi. 2021-05-21. Linear stability of the Couette flow in the 3D isentropic compressible Navier-Stokes equations. https://arxiv.org/abs/2105.10200

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