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Boundary value problems for two dimensional steady incompressible fluids. (English) Zbl 1478.35169

Summary: In this paper we study the solvability of different boundary value problems for the two dimensional steady incompressible Euler equation and for the magneto-hydrostatic equation. Two main methods are currently available to study those problems, namely the Grad-Shafranov method and the vorticity transport method. We describe for which boundary value problems these methods can be applied. The obtained solutions have non-vanishing vorticity.

MSC:

35Q31 Euler equations
76W05 Magnetohydrodynamics and electrohydrodynamics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35M12 Boundary value problems for PDEs of mixed type
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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