Existence Theory for Generalized Newtonian Fluids

ISBN-13: 9780128110447 / Angielski / Miękka / 2017 / 286 str.

Dominic Breit

Opis

Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs.

• Provides the state-of-the-art of the mathematical theory of Generalized Newtonian fluids
• Combines elliptic, parabolic and stochastic problems within existence theory under one umbrella
• Focuses on the construction of the solenoidal Lipschitz truncation, thus enabling readers to apply it to mathematical research
• Approaches stochastic PDEs with a perspective uniquely suitable for analysis, providing an introduction to Galerkin method for SPDEs and tools for compactness

Recenzje

"The main tools used in the book are related with Sobolev, Lebesgue and Orlicz spaces, with Bogovskii operator and with some special Korn-type inequalities...A large number of proofs and details are given, very useful for those interested in this field." --Zentralblatt MATH

Spis treści

Part 1: Stationary problems1: Preliminaries2: Fluid mechanics and Orlicz spaces3: Solenoidal Lipschitz truncation4: Prandtl-Eyring fluids

Part 2: Non-stationary problems5: Preliminaries6: Solenoidal Lipschitz truncation7: Power law fluids

Part 3: Stochastic problems8: Preliminaries9: Stochastic PDEs10: Stochastic power law fluids

Appendix A: Function spacesAppendix B: The A-Stokes systemAppendix C: Itô's formula in infinite dimensions

O autorze

Dominic Breit is currently Assistant Professor in the Department of Mathematics at Heriot Watt University, Edinburgh. In 2009, Breit finished his PhD study at Saarland University in Saarbrücken (Germany). In 2014, he was awarded a price for the best habilitation thesis at LMU Munich for a thesis which is the basis for this book.