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This book contains a first systematic study of compressible fluid
flows subject to stochastic forcing. The bulk is the existence of
dissipative martingale solutions to the stochastic compressible
Navier-Stokes equations. These solutions are weak in the
probabilistic sense as well as in the analytical sense. Moreover,
the evolution of the energy can be controlled in terms of the
initial energy. We analyze the behavior of solutions in short-time
(where unique smooth solutions exists) as well as in the long term
(existence of stationary solutions). Finally, we investigate the
asymptotics with respect to several parameters of the model based
on the energy inequality. Contents Part I: Preliminary results
Elements of functional analysis Elements of stochastic analysis
Part II: Existence theory Modeling fluid motion subject to random
effects Global existence Local well-posedness Relative energy
inequality and weak-strong uniqueness Part III: Applications
Stationary solutions Singular limits
Existence Theory for Generalized Newtonian Fluids provides a
rigorous mathematical treatment of the existence of weak solutions
to generalized Navier-Stokes equations modeling Non-Newtonian fluid
flows. The book presents classical results, developments over the
last 50 years of research, and recent results with proofs.
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