This monograph provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. For scalar hyperbolic conservation laws, the well posedness of the initial problem in the whole space as well as the initial boundary value problem in bounded domains is treated. Further, one of the first rigorous mathematical treatments of a class of non-Newtonian fluids is given. The new results, obtained here for both problems, have applications to many rapidly developing areas of physics, biology and mechanical engineering. Weak and Measure-valued Solutions to Evolutionary...

This volume consists of four contributions that are based on a series of lectures delivered by Jens Frehse. Konstantin Pikeckas, K.R. Rajagopal and Wolf von Wahl t the Fourth Winter School in Mathematical Theory in Fluid Mechanics, held in Paseky, Czech Republic, from December 3-9, 1995. In these papers the authors present the latest research and updated surveys of relevant topics in the various areas of theoretical fluid mechanics.
Specifically, Frehse and Ruzicka study the question of the existence of a regular solution to Navier-Stokes equations in five dimensions by means of weighted...