A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition - Shuai Xi (Communications in Analysis and Mechanics)
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 $ Ω\subseteq\mathbb{R}^{2} $, we derive a sufficient condition for the convergence to occur uniformly in time within the energy space $ L^{2}(Ω) $.