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Weak solutions for the Stokes system for compressible non‐Newtonian fluids with unbounded divergencePokorný, Milan; Szlenk, Maja
Mathematical methods in the applied sciences, 30 May 2023, Letnik: 46, Številka: 8Journal Article
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 L∞$$ {L}^{\infty } $$ 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$$ BMO $$ functions, which allowed us to adjust the method from Feireisl et al. (2015) to more relaxed conditions on the velocity.
