A jump discontinuity of compressible viscous flows grazing a non-convex corner

作者：Kweon Jae Ryong^*

来源：Journal de Mathematiques Pures et Appliquees, 2013, 100(3): 410-432.

DOI：10.1016/j.matpur.2013.01.007

• Compressible viscous flow
• Grazing corner
• Jump discontinuity

We show existence and regularity of solution for the compressible viscous steady state Navier-Stokes system on a polygon having a grazing corner and that the density has a jump discontinuity across a curve inside the domain. There are corresponding jumps in derivatives of the velocity. The solution comes from a well-posed boundary value problem on a polygonal domain with a non-convex corner. A formula for the decay of the jump is given. The decay formula suggests that density jumps can occur in a compressible flow with a non-vanishing viscosity.

• 出版日期2013-9