Large data existence theory for unsteady flows of fluids with pressure- and shear-dependent viscosities

摘要

A generalization of Navier Stokes' model is considered, where the Cauchy stress tensor depends on the pressure as well as on the shear rate in a power-law-like fashion, for values of the power-law index r is an element of (2d/d+2, 2]. We develop existence of generalized (weak) solutions for the resultant system of partial differential equations, including also the so far uncovered cases r is an element of (2d/d+2, 2d+2/d+2) and r = 2. By considering a maximal sensible range of the power-law index r, the obtained theory is in effect identical to the situation of dependence on the shear rate only. (C) 2015 Elsevier Ltd. All rights reserved.