A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum

Shujuan Wang, Jialin Ren and Rijian Su ()
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Shujuan Wang: College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China
Jialin Ren: College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China
Rijian Su: College of Computer and Communication Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China

Mathematics, 2024, vol. 12, issue 5, 1-10

Abstract: In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy ( ∥ ρ ∥ L ∞ ( 0 , T ; L ∞ ) + ∥ u ∥ C ( [ 0 , T ] ; L 3 ) < ∞ ) , then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over [ 0 , T ] . Notably, our analysis accommodates the presence of an initial vacuum.

Keywords: compressible magnetohydrodynamic equations; strong solution; blow up; vacuum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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