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This paper concerns the two-dimensional Euler equations with vortex-sheets initial data in half plane and in the domain Ω = {(x1, x2) : x2 ≥ γ(x1)}, γ(x1) = 0 for |x1| ≥ x0, x0 is a fixed constant, and γ(x1) is a sufficient smooth and simple curve. The Navier-Stokes approximations are constructed in this paper and by means of vanishing the viscosity, the global existence of weak solutions is obtained under the assumption that the initial vorticity is of one-sign. Navier boundary conditions are applied when constructing the Navier-Stokes approximations.

Navier-Stokes Approximations to 2D Vortex Sheets in Half Plane