Dominic Breit Poradie kníh

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

Focusing on the mathematical foundations of fluid dynamics, this book explores existence theory specifically for generalized Newtonian fluids. It delves into the complexities of fluid behavior under various conditions, addressing both theoretical and practical implications. The text presents rigorous proofs and methodologies, making it a valuable resource for researchers and students in applied mathematics and engineering. Through comprehensive analyses, it enhances the understanding of fluid mechanics and the mathematical challenges associated with non-Newtonian fluid models.