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 weakstrong uniqueness
Part III: Applications
Stationary solutions
Singular limits
D. Breit, Heriot-Watt University, UK;E. Feireisl, Czech Academy of Sciences, Czech Republic;M. Hofmanová, TU Berlin, Germany.
Schlagwörter zu:
Stochastically Forced Compressible Fluid Flows von Dominic Breit - mit der ISBN: 9783110490763
MAT003000 MATHEMATICS / Applied; SCI040000 SCIENCE / Physics / Mathematical & Computational; SCI041000 SCIENCE / Mechanics / General; SCI085000 SCIENCE / Mechanics / Fluids; SCI095000 SCIENCE / Mechanics / Hydrodynamics; Fluiddynamik; Kompressible Strömung; Navier-Stokes-Gleichung, Online-Buchhandlung
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