Utpal Manna, Akash Ashirbad Panda
Abstract:
In this article, we consider the ideal magnetic Benard problem in both two and
three dimensions and prove the existence and uniqueness of strong local-in-time
solutions, in Hs for s > (n/2)+1, n = 2,3. In addition, a necessary
condition is derived for singularity development with respect to the BMO-norm
of the vorticity and electrical current, generalizing the Beale-Kato-Majda condition
for ideal hydrodynamics.
Submitted June 3, 2018. Published September 7, 2020.
Math Subject Classifications: 76D03, 35B44, 35A01.
Key Words: Magnetic Benard problem; commutator estimates;
blow-up criterion; logarithmic Sobolev inequality.
DOI: 10.58997/ejde.2020.91
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Utpal Manna School of Mathematics Indian Institute of Science Education and Research Thiruvananthapuram, 695551, Kerala, India email: manna.utpal@iisertvm.ac.in |
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Akash Ashirbad Panda School of Mathematics Indian Institute of Science Education and Research Thiruvananthapuram, 695551, Kerala, India email: akash.panda13@iisertvm.ac.in, akashp595@gmail.com |
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