ABSTRACT
We study the Cauchy problem for the 2D incompressible magnetic Bénard fluid system with partial viscosity and derive some blow-up criteria of smooth solutions. More precisely, we first obtain a blow-up criterion of smooth solutions to the 2
D magnetic Bénard fluid system without zero magnetic diffusion and thermal diffusivity. Furthermore, we derive two blow-up criteria of smooth solutions to the 2
D magnetic Bénard fluid system without dissipation.
COMMUNICATED BY:
Acknowledgments
The authors would like to thank Professor Lili Du for many helpful discussions and suggestions. The authors would also like to thank the referee for his/her pertinent comments and advice.