The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons

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• 作者：Jae Ryong Kweon
• 关键词：Compressible viscous flows ; corner singularities ; Helmholtz decomposition ; regularity
• 刊名：Journal of Mathematical Fluid Mechanics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：19
• 期：1
• 页码：47-57
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics;
• 出版者：Springer International Publishing
• ISSN：1422-6952
• 卷排序：19

文摘

In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: \({{\rm {\bf u}}={\rm {\bf w}}+\nabla\varphi_R}\) with divw = 0 and a potential \({\varphi_R}\). Here w is the solution for the incompressible Stokes problem and \({\varphi_R}\) is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.