Two-dimensional Euler equations in an exterior domain.
The paper deals with the existence, uniqueness and regularity of global weak solutions to the two-dimensional Euler equations in an exterior domain \(\Omega\). Using the solutions of Navier-Stokes equations with modified Dirichlet boundary conditions as it was done by P. L. Lions in the case of bounded domains, the existence of global weak solutions when initial velocity is from \(L^2(\Omega)\) and initial vorticity is from \(L^r(\Omega),\) \(1<r\leq \infty,\) is proved. The local interior dependence on initial data, uniqueness and regularity of a weak solution are shown as well.
scientific article; zbMATH DE number 1900934
scientific article