Solvability of the leakage problem for the hydrodynamic Euler equations in Sobolev spaces
Abstract
The existence and uniqueness of solutions of the leakage problem in well posed boundary value problems for compressible and incompressible fluids in Sobolev spaces are proved. Leakage in a domain with smooth boundary, in a domain with edges, and in a two dimensional domain with edges is considered. The mixed problems for a compressible barotropic motion and of such motion in a nonsimply connected domain are also addressed. The trace theorem of a dihedral angle, the Dirichlet and Neumann problems for the Laplace equation in two dimensional domains with corners, and the mixed problem for a hyperbolic equation are examined.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1983
 Bibcode:
 1983STIN...8416485Z
 Keywords:

 Euler Equations Of Motion;
 Fluid Mechanics;
 Hydrodynamic Equations;
 Leakage;
 Problem Solving;
 Sobolev Space;
 Boundary Value Problems;
 Dirichlet Problem;
 Hyperbolic Differential Equations;
 Laplace Equation;
 Theorems;
 Fluid Mechanics and Heat Transfer