# American Institute of Mathematical Sciences

March  2019, 18(2): 569-602. doi: 10.3934/cpaa.2019029

## Well-posedness of axially symmetric incompressible ideal magnetohydrodynamic equations with vacuum under the non-collinearity condition

 School of Mathematics, Shanghai University of Finance and Economics, Shanghai Center of Mathematical Sciences, China

Received  November 2017 Revised  June 2018 Published  October 2018

Fund Project: The author is supported by NSFC grant 11601305.

We consider a free boundary problem for the axially symmetric incompressible ideal magnetohydrodynamic equations that describe the motion of the plasma in vacuum. Both the plasma magnetic field and vacuum magnetic field are tangent along the plasma-vacuum interface. Moreover, the vacuum magnetic field is composed in a non-simply connected domain and hence is non-trivial. Under the non-collinearity condition for the plasma and vacuum magnetic fields, we prove the local well-posedness of the problem in Sobolev spaces.

Citation: Xumin Gu. Well-posedness of axially symmetric incompressible ideal magnetohydrodynamic equations with vacuum under the non-collinearity condition. Communications on Pure & Applied Analysis, 2019, 18 (2) : 569-602. doi: 10.3934/cpaa.2019029
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