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

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.

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

Part 1: Stationary problems 1: Preliminaries 2: Fluid mechanics and Orlicz spaces 3: Solenoidal Lipschitz truncation 4: Prandtl-Eyring fluids

Part 2: Non-stationary problems 5: Preliminaries 6: Solenoidal Lipschitz truncation 7: Power law fluids

Part 3: Stochastic problems 8: Preliminaries 9: Stochastic PDEs 10: Stochastic power law fluids

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