Stochastic Shear Thickening Fluids:Strong Convergence of the Galerkin Approximation and the Energy Equality

Details Stochastic Shear Thickening Fluids:Strong Convergence of the Galerkin Approximation and the Energy Equality Stochastic Shear Thickening Fluids:Strong Convergence of the Galerkin Approximation and the Energy Equality

2010-09-11

arxiv.org/abs/1009.2136v1

Mathematics

Probability

Scientific paper

We consider a SPDE (stochastic partial differential equation) 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 focus on the shear thickening case, more precisely, on the case: $p \in [1 +{d \over 2}, {2d \over d-2})$, where $d$ is the dimension of the space. We prove that the Galerkin scheme approximates the the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.

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