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

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