Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 42, Issue 5, Pages 2333-2353Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2021192
Keywords
magnetohydrodynamics; Boussinesq; axially symmetric; regularity criteria; velocity
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Funding
- Natural Science Foundation of Jiangsu Province [BK20200803, BK20180414]
- National Natural Science Foundation of China [12001285, 11801268, 12031006]
- Startup Foundation for Introducing Talent of NUIST [2019r033]
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The paper discusses regularity criteria of a class of 3D axially symmetric MHD-Boussinesq systems without magnetic resistivity or thermal diffusivity. By making certain critical assumptions on the horizontal angular component of the velocity, it is shown that the system's solutions can be smoothly extended beyond the blow-up time if the magnetic field contains only the horizontal swirl component. No prior assumptions are made on the magnetic field or the temperature fluctuation.
In this paper, we consider regularity criteria of a class of 3D axially symmetric MHD-Boussinesq systems without magnetic resistivity or thermal diffusivity. Under some Pro di-Serrin type critical assumptions on the horizontal angular component of the velocity, we will prove that strong solutions of the axially symmetric MHD-Boussinesq system can be smoothly extended beyond the possible blow-up time T-* if the magnetic field contains only the horizontal swirl component. No a priori assumption on the magnetic field or the temperature fluctuation is imposed.
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