Stochastic power law fluids: Existence and uniqueness of weak solutions

Abstract

We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.

Published in at http://dx.doi.org/10.1214/10-AAP741 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Stochastic shear thickening fluids: Strong convergence of the Galerkin approximation and the energy equality

Cited by in corpus (6)

• Local and global well-posedness of SPDE with generalized coercivity conditions
• Existence theory for stochastic power law fluids
• Stochastic shear thickening fluids: Strong convergence of the Galerkin approximation and the energy equality
• An averaged space-time discretization of the stochastic $p$-Laplace system
• Regularity theory for nonlinear systems of SPDEs
• Kolmogorov Equations for Randomly Perturbed Generalized Newtonian Fluids