Communications in Mathematical Sciences

Volume 14 (2016)

Number 8

Existence of axially symmetric weak solutions to steady MHD with nonhomogeneous boundary conditions

Pages: 2287 – 2307



Shangkun Weng (Pohang Mathematics Institute, Pohang University of Science and Technology, Pohang, Gyungbuk, Korea)


We establish the existence of axially symmetric weak solutions to steady incompressible magnetohydrodynamics with nonhomogeneous boundary conditions. The key issue is the Bernoulli’s law for the total head pressure $\Phi = \frac{1}{2} ({\lvert u \rvert}^2 + {\lvert h \rvert}^2) + p$ to a special class of solutions to the inviscid, non-resistive MHD system, where the magnetic field only contains the swirl component.


existence, MHD equations, axially symmetric, Bernoulli’s law

2010 Mathematics Subject Classification

35Q35, 76D05

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Published 26 October 2016