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978-3-8439-0956-3, Reihe Mathematik

Martin Sauer Existence and Uniqueness Results for Randomly Forced Generalized Newtonian Fluids

146 Seiten, Dissertation Technische Universität Darmstadt (2013), Hardcover, A5

The subject of this thesis is the analysis of nonlinear stochastic partial differential equations (SPDEs) arising from the theory of mathematical fluid dynamics, in particular generalizations of the well-known stochastic Navier-Stokes equations to so-called Non-Newtonian fluids. Existence and uniqueness of solutions to such SPDEs is studied within the so-called variational approach, especially a recent improvement that covers nonlinear drifts with locally monotone coefficients. Following this, we analyze quantitative and qualitative aspects of invariant measures for the transition semigroup associated to such SPDEs. Finally, we are able to study the associated backward Kolmogorov equation for the following two problems in two space dimensions. The first one concerns Non-Newtonian fluids perturbed by a smooth noise, the second one the stochastic Navier-Stokes equations in a rotating frame with so-called space-time white noise and invariant measure given by the enstrophy.