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

• Published in: Communications in analysis and mechanics Vol. 16; no. 4; pp. 896 - 909
• Main Author: Xi, Shuai
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: no-slip boundary condition; nonhomogeneous ns system; the vanishing viscosity limit
• ISSN: 2836-3310; 2836-3310
• DOI: 10.3934/cam.2024039

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 [<xref ref-type="bibr" rid="b1">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) $.