Existence and equivalence of solutions of mixed problems for Euler's hydrodynamic equations

Zajaczkowski's thesis on the solvability of the leakage problem for the nonstationary Euler equations in Sobolev spaces is summarized. Mixed problems for Euler's equations are analyzed. The fundamental problem of hydrodynamics is reviewed, and the issues of flow of an ideal fluid are examined. Mathematical bases of fluid mechanics are formulated. Hypotheses concerning the existence, equivalence, and regularity of solutions of the Dirichlet problem are discused, among others. The Holder spaces, Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Green's functions, and the Schauders estimates for solutions of elliptic boundary value problems involving a dihedral angle are discussed.