PDE models for chemotaxis and hydrodynamics in supercritical function spaces (Q518689)

This book deals with a systematic study of two model examples of evolution equations featuring dissipation and nonlinear transport terms: the Keller-Segel and the Navier-Stokes systems. The main interest is in the applications of the theory of (inhomogeneous) function spaces of Besov-Sobolev-Lizorkin-Triebel type to the questions of the (global in time) existence, stability, regularity and decay properties of solutions. Besides those two basic examples, various modifications of biological and hydrodynamical models are studied including Fokker-Planck equations, models with logistic terms and for competing species, and chemotaxis Navier-Stokes equations. The list of references is rather extensive (but not exhaustive).