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 v ⋅ n = a , 2 D ( v ) n ⋅ s + α v ⋅ s = b , where the tensor D ( v ) is the rate of strain of the fluid’s velocity v and (n , s) 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.