A Kato-Type Criterion for the Inviscid Limit of the Compressible Navier–Stokes System

Yonghui Zou; Xin Xu

doi:10.1007/s00021-023-00798-4

A Kato-Type Criterion for the Inviscid Limit of the Compressible Navier–Stokes System

Yonghui Zou, Xin Xu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We study the inviscid limit of the compressible Navier–Stokes system with no-slip boundary condition in a smooth bounded domain Ω ⊆ R² . Inspired by the work of (Sueur in J Math Fluid Mech 16:163–178, 2014; Constantin et al. in Proc Am Math Soc 143:3075–3090, 2015), we obtain a sufficient condition for the convergence of the solution of the compressible Navier–Stokes equations to the solution of the compressible Euler equations in the energy space L²(Ω) uniformly in time.

Original language	English
Article number	45
Journal	Journal of Mathematical Fluid Mechanics
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s00021-023-00798-4
State	Published - Aug 2023
Externally published	Yes

Keywords

Boundary layer
Compressible Navier–Stokes equations
Inviscid limit

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10.1007/s00021-023-00798-4

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abstract = "We study the inviscid limit of the compressible Navier–Stokes system with no-slip boundary condition in a smooth bounded domain Ω ⊆ R2 . Inspired by the work of (Sueur in J Math Fluid Mech 16:163–178, 2014; Constantin et al. in Proc Am Math Soc 143:3075–3090, 2015), we obtain a sufficient condition for the convergence of the solution of the compressible Navier–Stokes equations to the solution of the compressible Euler equations in the energy space L2(Ω) uniformly in time.",

keywords = "Boundary layer, Compressible Navier–Stokes equations, Inviscid limit",

author = "Yonghui Zou and Xin Xu",

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AU - Xu, Xin

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N2 - We study the inviscid limit of the compressible Navier–Stokes system with no-slip boundary condition in a smooth bounded domain Ω ⊆ R2 . Inspired by the work of (Sueur in J Math Fluid Mech 16:163–178, 2014; Constantin et al. in Proc Am Math Soc 143:3075–3090, 2015), we obtain a sufficient condition for the convergence of the solution of the compressible Navier–Stokes equations to the solution of the compressible Euler equations in the energy space L2(Ω) uniformly in time.

AB - We study the inviscid limit of the compressible Navier–Stokes system with no-slip boundary condition in a smooth bounded domain Ω ⊆ R2 . Inspired by the work of (Sueur in J Math Fluid Mech 16:163–178, 2014; Constantin et al. in Proc Am Math Soc 143:3075–3090, 2015), we obtain a sufficient condition for the convergence of the solution of the compressible Navier–Stokes equations to the solution of the compressible Euler equations in the energy space L2(Ω) uniformly in time.

KW - Boundary layer

KW - Compressible Navier–Stokes equations

KW - Inviscid limit

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A Kato-Type Criterion for the Inviscid Limit of the Compressible Navier–Stokes System

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Keywords

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