Solvability of the leakage problem for the hydrodynamic Euler equations in Sobolev spaces

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.