On the critical one-component velocity regularity criteria to 3-D incompressible MHD system

DOI10.1016/j.jde.2016.01.023zbMath1350.35156arXiv1509.05531OpenAlexW2963792960MaRDI QIDQ5964044

Yanlin Liu

Publication date: 26 February 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05531

zbMATH Keywords

magnetohydrodynamicsglobal regularityanisotropic Littlewood-Paley theory

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Maximal functions, Littlewood-Paley theory (42B25) Magnetohydrodynamics and electrohydrodynamics (76W05) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Blow-up in context of PDEs (35B44)

Related Items (7)

Regularity criteria for 3D MHD equations via mixed velocity-magnetic gradient tensors ⋮ Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system ⋮ On the Navier-Stokes equations in scaling-invariant spaces in any dimension ⋮ On conditional regularity for the MHD equations via partial components ⋮ On the critical blow up criterion with one velocity component for 3D incompressible MHD system ⋮ A logarithmically improved regularity criterion for the $3$D MHD system involving the velocity field in homogeneous Besov spaces ⋮ Remarks on the global regularity issue of the two-and-a-half-dimensional Hall-magnetohydrodynamics system

Cites Work

• On the critical one component regularity for 3-D Navier-Stokes system: general case
• Two regularity criteria for the 3D MHD equations
• On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations
• Anisotropic Navier-Stokes equation in critical spaces
• Fourier Analysis and Nonlinear Partial Differential Equations
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires

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