Stochastically Forced Compressible Fluid Flows
Jan 2018 · De Gruyter Series in Applied and Numerical Mathematics Book 3 · Walter de Gruyter GmbH & Co KG
Ebook
342
Pages
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About this ebook
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
About the author
D. Breit, Heriot-Watt University, UK; E. Feireisl, Czech Academy of Sciences, Czech Republic; M. Hofmanová, TU Berlin, Germany.
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