Solvability of an initial boundary value problem for the Euler equations in twodimensional domain with corners

The aim of this paper is to prove the existence and uniqueness of local solutions of some initial-boundary-value problems for the Euler equations of an incompressible fluid in a bounded domain with corners. Two cases of a nonvanishing normal component of velocity on the boundary are considered. The relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. Two initial-boundary-value problems for the Euler equations are formulated; the existence and uniqueness of solutions of the Laplace equation in two-dimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces; and the existence and uniqueness of the solutions are proven using the method of successive approximations.