Global Regularity of 2-D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: High Regularity Case
Year: 2019
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 163–191
Abstract
This paper is a continuation work of [26] and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow. We assume the initial density $\rho_0=\eta_1{1}_{\Omega_0}+\eta_2{1}_{\Omega_0^c}$, where $(\eta_1,\eta_2)$ is any pair of positive constants and $\Omega_0$ is a bounded, simply connected domain with $W^{k+2,p}(R^2)$ boundary regularity. We prove that for any positive time $t$, the density function $\rho(t)=\eta_1{1}_{\Omega(t)}+\eta_2{1}_{\Omega(t)^c}$, and the domain $\Omega(t)$ preserves the $W^{k+2,p}$-boundary regularity.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0004
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 163–191
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Inhomogeneous incompressible Navier-Stokes equations density patch striated distributions Littlewood-Paley theory.
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