Large Time Existence of Special Strong Solutions to MHD Equations in Cylindrical Domains
We investigate the problem of the existence of regular solutions to the three-dimensional MHD equations in cylindrical domains with perfectly conducting boundaries and under the Navier boundary conditions for the velocity field. We show that if the initial and external data do not change too rapidly along the axis of the cylinder, then there exists a unique regular solution for any finite time.
KeywordsStrong solutions MHD equations Large data
Mathematics Subject Classification35Q35 76W05
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement No. 319012 and from the Funds for International Co-operation under Polish Ministry of Science and Higher Education Grant Agreement No. 2853/7.PR/2013/2.
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Conflict of interest
The authors declare that they have no conflict of interest.
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