Unique solvability for the density-dependent Navier–Stokes equations

详细信息	查看全文 | 推荐本文 |

• 作者：Cho ; Yonggeun ; Kim ; Hyunseok
• 关键词：76N10 ; Navier&ndash ; Stokes equations ; Density-dependent viscosity ; Strong solution ; Vacuum
• 刊名：Nonlinear Analysis
• 出版年：2004
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：November, 2004
• 卷：59
• 期：4
• 页码：465-489
• 文件大小：304 K

摘要

In this paper we consider the incompressible Navier–Stokes equations with a density-dependent viscosity in a bounded domain Formula Not Shown of Formula Not Shown . We prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition. This condition is also necessary for a very general initial data. Moreover, we provide a blow-up criterion for the regularity of the strong solution. For these results, the initial density need not be strictly positive. It may vanish in an open subset of Formula Not Shown .