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

Autor: Pokorný, Milan, Szlenk, Maja
Rok vydání: 2022
Předmět:
Druh dokumentu: Working Paper
DOI: 10.1002/mma.9083
Popis: We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack of the $L^\infty$ 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 $BMO$ functions, which allowed us to adjust the method from (Feireisl et al., 2015) to more relaxed conditions on the velocity.
Databáze: arXiv