Liouville theorems for stationary flows of generalized Newtonian fluids (Q2915669)

This report concerns the generalized Navier-Stokes equations -- the viscosity (appearing as a factor in the deviatoric stress tensor) depends on the symmetric part of the velocity gradient. It contains 4 interesting papers, two submitted by the author and two joint articles published with \textit{M. Fuchs} [Calc. Var. Partial Differ. Equ. 44, No. 1--2, 271--295 (2012; Zbl 1252.49075); J. Math. Sci., New York 185, No. 5, 746-753 (2012); translation from Zap. Nauchn. Semin. POMI 397, 157--171 (2011; Zbl 1278.35243)].NEWLINENEWLINEThe content related with the shear thickening fluids in the 2D case -- the deviatoric stress tensor is the gradient of a potential \(H\) and the viscosity is an increasing function related with \(H\). The main results are: 1) The proof of a conjecture given by Martin Fuchs, where a Liouville theorem is obtained, by removing a previous hypothesis on the velocity behaviour at infinity; 2) An entire weak solution, satisfying some regularity hypothesis, is zero.