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# 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

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n8.a8

#### Author

#### Abstract

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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

35Q35, 76D05