Beale-Kato-Majda's criterion for magneto-hydrodynamic equations with zero viscosity

DOI10.30755/NSJOM.09142zbMath1464.35205OpenAlexW2974855866MaRDI QIDQ4985330

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Publication date: 23 April 2021

Published in: Novi Sad Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.30755/nsjom.09142

zbMATH Keywords

magneto-hydrodynamic equations with zero viscosity\( \dot{B}_{\infty\infty }^0\) space

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Magnetohydrodynamics and electrohydrodynamics (76W05) Blow-up in context of PDEs (35B44)

Cites Work

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• A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosity
• On the regularity criterion of weak solutions for the 3D MHD equations
• On the blow-up criterion of smooth solutions to the 3D ideal MHD equations
• BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
• A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field
• Regularity criteria for the solutions to the 3D MHD equations in the multiplier space
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD
• On blow-up criteria of smooth solutions to the 3-D Euler equations in a bounded domain.
• On the blow-up criterion of smooth solutions to the MHD system in BMO space
• Blow up criterion of smooth solutions to the MHD equations in Besov spaces
• Some mathematical questions related to the mhd equations
• Commutator estimates and the euler and navier-stokes equations
• Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations
• Incompressible flows of an ideal fluid with unbounded vorticity

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