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Breit, Dominic / Feireisl, Eduard / Hofmanová, Martina

Stochastically Forced Compressible Fluid Flows

Series:De Gruyter Series in Applied and Numerical Mathematics 3

    99,95 € / $114.99 / £91.00*

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    Publication Date:
    January 2018
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    Aims and Scope

    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.

    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


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    D. Breit, Heriot-Watt University, UK; E. Feireisl, Czech Academy of Sciences, Czech Republic; M. Hofmanová, TU Berlin, Germany.

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