arrow
Volume 35, Issue 2
Global Regularity of 2-D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: High Regularity Case

Xian Liao & Ping Zhang

Anal. Theory Appl., 35 (2019), pp. 163-191.

Published online: 2019-04

[An open-access article; the PDF is free to any online user.]

Export citation
  • 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.

  • AMS Subject Headings

35Q30, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{ATA-35-163, author = {}, title = {Global Regularity of 2-D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: High Regularity Case}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0004}, url = {http://global-sci.org/intro/article_detail/ata/13112.html} }
TY - JOUR T1 - Global Regularity of 2-D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: High Regularity Case JO - Analysis in Theory and Applications VL - 2 SP - 163 EP - 191 PY - 2019 DA - 2019/04 SN - 35 DO - http://doi.org/10.4208/ata.OA-0004 UR - https://global-sci.org/intro/article_detail/ata/13112.html KW - Inhomogeneous incompressible Navier-Stokes equations, density patch, striated distributions, Littlewood-Paley theory. AB -

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.

Xian Liao & Ping Zhang. (2019). Global Regularity of 2-D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: High Regularity Case. Analysis in Theory and Applications. 35 (2). 163-191. doi:10.4208/ata.OA-0004
Copy to clipboard
The citation has been copied to your clipboard