Essential m-dissipativity of Kolmogorov operators for the 2D-stochastic shear thickening fluids
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We study a class of viscous, incompressible non-Newtonian fluids in two space dimensions with periodic boundary conditions and an additive Gaussian noise. The nonlinear elliptic operator related to the stress tensor possesses p-structure. When the fluid is shear thickening, we prove that the associated Kolmogorov operator is essentially m-dissipative in a space with respect to an invariant measure. In addition, if the viscosity constant is sufficiently large, we show that the invariant measure is exponential mixing so that it is also unique.
KeywordsNon-Newtonian fluid Kolmogorov operator Dissipativity Invariant measure
Mathematics Subject ClassificationPrimary 60H15 76A05 Secondary 47H06 37L40
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