A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition

Shuai Xi; Shuai Xi

doi:10.3934/cam.2024039

Communications in Analysis and Mechanics

2024, Volume 16, Issue 4: 896-909. doi: 10.3934/cam.2024039

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A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition

Shuai Xi ^{1,2
,
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1.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China

Received: 14 March 2024 Revised: 17 April 2024 Accepted: 15 July 2024 Published: 05 December 2024
35B40, 35L60

The objective of this paper is to examine the vanishing viscosity limit of the nonhomogeneous incompressible NS systerm, subject to the no-slip boundary condition. By adopting Kato's approach of constructing an artificial boundary layer ^[1], within a smooth and bounded domain designated as $ \Omega\subseteq\mathbb{R}^{2} $, we derive a sufficient condition for the convergence to occur uniformly in time within the energy space $ L^{2}(\Omega) $.
- nonhomogeneous NS system,
- the vanishing viscosity limit,
- no-slip boundary condition
Citation: Shuai Xi. A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition[J]. Communications in Analysis and Mechanics, 2024, 16(4): 896-909. doi: 10.3934/cam.2024039

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Abstract

The objective of this paper is to examine the vanishing viscosity limit of the nonhomogeneous incompressible NS systerm, subject to the no-slip boundary condition. By adopting Kato's approach of constructing an artificial boundary layer ^[1], within a smooth and bounded domain designated as $ \Omega\subseteq\mathbb{R}^{2} $, we derive a sufficient condition for the convergence to occur uniformly in time within the energy space $ L^{2}(\Omega) $.

References

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