Euler equations with non-homogeneous Navier slip boundary conditions

We consider the flow of an ideal fluid in a 2D bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with non-homogeneous Navier slip boundary conditions. These conditions can be written in the form , , where the tensor is the rate of strain of the fluid’s velocity and is the pair formed by the normal and tangent vectors to the boundary. We establish the solvability of this problem for the class of solutions with L_p-bounded vorticity, p∈(2,∞]. To prove the solvability we realize the passage to the limit in Navier-Stokes equations with vanishing viscosity.