Stochastically Forced Compressible Fluid Flows – eBook PDF
This ebook Stochastically Forced Compressible Fluid Flows (PDF) 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 energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exist) 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.
Part 1: Preliminary results Elements of functional analysis Elements of stochastic analysis
Part 2: Existence theory Modeling fluid motion subject to random effects Global existence Local well-posedness Relative energy inequality and weak–strong uniqueness
Part 3: Applications Stationary solutions Singular limits
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