ON GENERALIZED STOKES’ AND BRINKMAN’S EQUATIONS WITH PRESSURE- AND SHEAR-DEPENDENT VISCOSITY AND DRAG COEFFICIENT

by · Sep 23, 2014 · 831 views ·

Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic We study generalizations of the Darcy, Forchheimer, Brinkman and Stokes problem in which the viscosity and the drag coefficient depend on the shear rate and the pressure. We focus on existence of weak solutions to the problem, with the chief aim to capture as wide a group of viscosities and drag coefficients as mathematically feasible and to provide a theory that holds under minimal, not very restrictive conditions. Even in the case of generalized Stokes system, the established result answers a question on existence of weak solutions that has been open so far.

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