On the Global Solvability of the Two-Dimensional Through-Flow Problem for the Euler Equations with Unbounded Vorticity at the Entrance

We consider the global solvability of the two-dimensional through-flow problem for an ideal incompressible fluid with restrictions for the smoothness of the input data and solution (especially, for the vorticity) as weak as possible. The normal component of the velocity is prescribed on the whole boundary of the flow domain and the vorticity is prescribed at the entrance. It is shown that the global existence theorem can be proved in the class $\{{\rm rot}\,\boldsymbol{u} \in L_{\alpha}\}$ as $\alpha>4/3$, using the regularization of the input data and compactness arguments.