Boundary Value Problems in Mechanics of Nonhomogeneous Fluids (Studies in Mathematics and its Applications)

The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations. The investigations involve the results concerning Navier-Stokes equations of viscous heat-conductive gas, incompressible nonhomogeneous fluid and filtration of multi-phase mixture in a porous medium. The correctness of the initial boundary-value problems and the qualitative properties of solutions are also considered. The book is written for those who are interested in the theory of nonlinear partial differential equations and their applications in mechanics. The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations.

The investigations involve the results concerning Navier-Stokes equations of viscous heat-conductive gas, incompressible nonhomogeneous fluid and filtration of multi-phase mixture in a porous medium. The correctness of the initial boundary-value problems and the qualitative properties of solutions are also considered. The book is written for those who are interested in the theory of nonlinear partial differential equations and their applications in mechanics. Content: Edited by Pages ii-iii Copyright page Page iv Preface Pages v-vii Chapter 1 Models of the Dynamics OP Heterogeneous Media and the Body of Mathematics Pages 1-37 Chapter 2 Correctness “IN THE WHOLE” of the Boundary Problems for Equations of One-Dimensional Non-Stationary Motion of a Viscous Gas Pages 39-100 Chapter 3 Initial-Boundary Value Problems for the Navier-Stokes Equations of a Nonhomogeneous Viscous Incompressible Fluid Pages 101-148 Chapter 4 Correctness of the Problem of Flowing Through for the of an Ideal Incompressible Liquid Pages 149-197 Filtration of Immiscible Liquids Pages 199-295 Literature Pages 297-309