Existence of solutions to the nonhomogeneous steady Magnetohydrodynamic equations

Abstract

We study the nonhomogeneous boundary value problem for the steady Magnetohydrodynamic equations in a two-dimensional bounded domain with multiply connected boundary. We prove that this problem has an admissible solution in an admissible domain if the boundary value is admissible. The proof of the main result uses some property for a weak solution to the transport equations in an admissible domain.

Keywords:

• MHD
• existence
• bounded domain

AMS Subject Classifications:

• 35D30

Acknowledgements

I would like to thank Professor Changshou Lin at National Taiwan University.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 If a is boundary value on then for any there exists the extension of boundary value a as holds. where .