Ebook: PDE Models for Chemotaxis and Hydrodynamics in Supercritical Function Spaces

This book deals with PDE models for chemotaxis (the movement of biological cells or organisms in response of chemical gradients) and hydrodynamics (viscous, homogeneous, and incompressible fluid filling the entire space). The underlying Keller Segel equations (chemotaxis), Navier Stokes equations (hydrodynamics), and their numerous modifications and combinations are treated in the context of inhomogeneous spaces of Besov Sobolev type. The author pays special attention to mapping properties of related nonlinearities. Further models are considered, including (deterministic) Fokker Planck equations and chemotaxis Navier Stokes equations. These notes are addressed to graduate students and mathematicians with a working knowledge of basic elements of the theory of function spaces, especially of Besov Sobolev type, and an interest in mathematical biology and physics. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society