Stochastically Forced Compressible Fluid Flows

✍ Scribed by Dominic Breit; Eduard Feireisl; Martina Hofmanová

• Publisher: De Gruyter
• Year: 2018
• Tongue: English
• Leaves: 344
• Series: De Gruyter Series in Applied and Numerical Mathematics; 3
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Acknowledgements
Notation
Contents
Part I: Preliminary results
1. Elements of functional analysis
2. Elements of stochastic analysis
Part II: Existence theory
3. Modeling fluid motion subject to random effects
4. Global existence
5. Local well-posedness
6. Relative energy inequality and weak–strong uniqueness
Part III: Applications
7. Stationary solutions
8. Singular limits
A. Appendix
B. Bibliographical remarks
Index