Weak solutions for the Stokes system for compressible non‐Newtonian fluids with unbounded divergence

Abstract

We investigate the existence of weak solutions to a certain system of partial differential equations, modeling the behavior of a compressible non‐Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack of the estimate on the divergence of the velocity field. The result was obtained by combining the regularity theory for singular operators with a certain logarithmic integral inequality for functions, which allowed us to adjust the method from Feireisl et al. (2015) to more relaxed conditions on the velocity.