Stochastically Forced Compressible Fluid Flows
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About this book
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
Author / Editor information
D. Breit, Heriot-Watt University, UK; E. Feireisl, Czech Academy of Sciences, Czech Republic; M. Hofmanová, TU Berlin, Germany.
Reviews
"This book is very well written and rigorously presented, and constitutes a significant contribution to the field. It is very well motivated by various interesting and important applications in fluid mechanics and related areas. The book is recommended to all researchers interested by the modern theory of compressible fluid flows."
Mirela Kohr in: Mathematical Reviews Clippings April 2019 MR3791804
Topics
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Frontmatter
I -
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Acknowledgements
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Notation
VII -
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Contents
IX - Part I: Preliminary results
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1. Elements of functional analysis
3 -
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2. Elements of stochastic analysis
21 - Part II: Existence theory
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3. Modeling fluid motion subject to random effects
81 -
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4. Global existence
101 -
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5. Local well-posedness
187 -
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6. Relative energy inequality and weak–strong uniqueness
217 - Part III: Applications
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7. Stationary solutions
235 -
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8. Singular limits
271 -
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A. Appendix
305 -
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B. Bibliographical remarks
317 -
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Index
327
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