Existence Theory for Generalized Newtonian Fluids

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.

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

Scientists and graduate students with basic knowledge in nonlinear partial differential equations and interest in mathematical fluid mechanics

• 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