Navier-Stokes Equations in Irregular Domains

The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations in weighted Sobolev and Hölder spaces, and the investigation of the smoothness of their solutions. This allows one to deal with the special problems that arise in the presence of edges or angular points in the plane case, at the boundary or noncompact boundaries. Such problems cannot be dealt with in any of the usual ways.
Audience : Graduate students, research mathematicians and hydromechanicians whose work involves functional analysis and its applications to Navier-Stokes equations.

Klappentext

The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations in weighted Sobolev and Hölder spaces, and the investigation of the smoothness of their solutions. This allows one to deal with the special problems that arise in the presence of edges or angular points in the plane case, at the boundary or noncompact boundaries. Such problems cannot be dealt with in any of the usual ways. Audience: Graduate students, research mathematicians and hydromechanicians whose work involves functional analysis and its applications to Navier-Stokes equations.

Inhalt

1. Preliminaries.- 2. Boundary Value Problems for the Stokes System.- 3. Boundary Value Problems in Plane and Bihedral Angles.- 4. The First Boundary Value Problem in a Given Domain.- 5. Steady Motion of a Fluid with a Free Surface.- Appendix 1. The Green Matrices on the Half-Space and Half-Plane.- 1. The Green Matrices on the Half-Space.- 2. The Green Matrices on the Half-Plane.- Appendix 2. Weighted Schauder Estimates of Solutions to Elliptic Boundary Value Problems.- 1. Function Spaces.- 2. Estimates of the Solution of the Boundary Value Problem in the Half-Space.- 3. Representation of the Solution to the Boundary Value Problem in the Half-Space.- 4. The Boundary Value Problem in a Bounded Domain.- References.- Notation Index.