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. ContentsPart Preliminary resultsElements of functional analysisElements of stochastic analysis Part Existence theoryModeling fluid motion subject to random effectsGlobal existenceLocal well-posednessRelative energy inequality and weak-strong uniqueness Part ApplicationsStationary solutionsSingular limits

Stochastically Forced Compressible Fluid Flows (De Gruyter Series in Applied and Numerical Mathematics) PDF

The list of books you might like