WIAS Preprint No. 2786, (2020)
Analysis of a compressible Stokes-flow with degenerating and singular viscosity
- Farshbaf Shaker, Mohammad Hassan
- Thomas, Marita
2010 Mathematics Subject Classification
- 35D30 35Q35 35K92 35J70 76Nxx 76M30
- Suspensions, compressible flows, degenerate and singular problems
In this paper we show the existence of a weak solution for a compressible single-phase Stokes flow with mass transport accounting for the degeneracy and the singular behavior of a density-dependent viscosity. The analysis is based on an implicit time-discrete scheme and a Galerkin-approximation in space. Convergence of the discrete solutions is obtained thanks to a diffusive regularization of p-Laplacian type in the transport equation that allows for refined compactness arguments on subdomains.