Global regularity of 2D almost resistive MHD equations

DOI10.1016/j.nonrwa.2017.10.006zbMath1406.35080arXiv1602.04549OpenAlexW2964165764MaRDI QIDQ1698345

Jiefeng Zhao, Bao-Quan Yuan

Publication date: 15 February 2018

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.04549

zbMATH Keywords

nonlinear maximal principles

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Maximum principles in context of PDEs (35B50) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items (37)

On well-posedness and blow-up criterion for the 2D tropical climate model ⋮ Global Well-Posedness of the 2D MHD Equations of Damped Wave Type in Sobolev Space ⋮ Global existence of strong solutions to the multi-dimensional inhomogeneous incompressible MHD equations ⋮ Global regularity of 2D incompressible Leray-alpha-MHD equations with only magnetic diffusion ⋮ Global regularity for a class of 2D tropical climate model ⋮ Global Existence and Time-decay Rates of Solutions to 2D Magneto-micropolar Fluid Equations with Partial Viscosity ⋮ Global regularity of the generalized liquid crystal model with fractional diffusion ⋮ Remark on the global regularity of 2D MHD equations with almost Laplacian magnetic diffusion ⋮ Global regularity for solutions to 2D generalized MHD equations with multiple exponential upper bound uniformly in time ⋮ Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction ⋮ Global regularity of 2D MHD equations with almost Laplacian velocity dissipation ⋮ Global Solutions to 3D Incompressible MHD System with Dissipation in Only One Direction ⋮ Mild ill-posedness in \(L^\infty\) for 2D magnetohydrodynamic system with damping ⋮ The 2D magnetohydrodynamic system with Euler‐like velocity equation and partial magnetic diffusion ⋮ Stabilizing effect of the magnetic field and large-time behavior of 2D incompressible MHD system with vertical dissipation ⋮ Stability for a system of 2D incompressible anisotropic magnetohydrodynamic equations ⋮ Beyond the BKM criterion for the 2D resistive magnetohydrodynamic equations ⋮ Stability and exponential decay for magnetohydrodynamic equations ⋮ Global existence and uniqueness of the 2D damped wave-type MHD equations ⋮ Unique weak solutions of the magnetohydrodynamic equations with fractional dissipation ⋮ Stability and optimal decay for the 3D magnetohydrodynamic equations with only horizontal dissipation ⋮ Optimal decay rates for \(n\)-dimensional generalized magnetohydrodynamic equations ⋮ Global regularity for the 2D magnetic Bénard fluid system with mixed partial viscosity ⋮ Stabilization of a Background Magnetic Field on a 2 Dimensional Magnetohydrodynamic Flow ⋮ A class large solution of the 2D MHD equations with velocity and magnetic damping ⋮ Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium ⋮ Smoothing and stabilization effects of magnetic field on electrically conducting fluids ⋮ Global regularity of the 2D magnetohydrodynamic equations with fractional anisotropic dissipation ⋮ On regularity criteria of the 2D generalized MHD equations ⋮ Global well-posedness of 3D magneto-micropolar fluid equations with mixed partial viscosity near an equilibrium ⋮ The resistive magnetohydrodynamic equation near an equilibrium ⋮ Global smooth solutions of the generalized MHD equations with large initial data ⋮ Global existence and large time behavior of solutions to 3D MHD system near equilibrium ⋮ A new regularity criterion of the 2D MHD equations ⋮ Global regularity of 2D temperature-dependent MHD-Boussinesq equations with zero thermal diffusivity ⋮ Influence of a background magnetic field on a 2D magnetohydrodynamic flow ⋮ A class of global large solutions to the magnetohydrodynamic equations with fractional dissipation

Cites Work

• Unnamed Item
• Global regularity for a class of generalized magnetohydrodynamic equations
• On global regularity of 2D generalized magnetohydrodynamic equations
• On the global regularity of two-dimensional generalized magnetohydrodynamics system
• Global Cauchy problem of 2D generalized MHD equations
• Global small solutions of 2-D incompressible MHD system
• Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
• BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
• Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD
• Generalized MHD equations.
• A maximum principle applied to quasi-geostrophic equations
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion
• A remark on global regularity of 2D generalized magnetohydrodynamic equations
• Remarks on global regularity of 2D generalized MHD equations
• Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion
• Global regularity of 2D generalized MHD equations with magnetic diffusion
• Vorticity and Incompressible Flow
• Some mathematical questions related to the mhd equations
• The 2D magnetohydrodynamic equations with magnetic diffusion
• Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation
• Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case
• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion

This page was built for publication: Global regularity of 2D almost resistive MHD equations