The 3D incompressible magnetohydrodynamic equations with fractional partial dissipation

DOI10.1016/j.jde.2018.07.046zbMath1403.35246OpenAlexW2884131553MaRDI QIDQ1993979

Wanrong Yang, Jiahong Wu, Quan-sen Jiu

Publication date: 6 November 2018

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

Full work available at URL: https://doi.org/10.1016/j.jde.2018.07.046

zbMATH Keywords

global regularityfractional partial dissipation3D magnetohydrodynamic equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Fractional partial differential equations (35R11)

Related Items (23)

Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping ⋮ Global Well-Posedness of the 2D MHD Equations of Damped Wave Type in Sobolev Space ⋮ Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction ⋮ Global existence of the strong solution to the 3D incompressible micropolar equations with fractional partial dissipation ⋮ The 2D magnetohydrodynamic system with Euler‐like velocity equation and partial magnetic diffusion ⋮ Stability and sharp decay for 3D incompressible MHD system with fractional horizontal dissipation and 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 ⋮ Stability and exponential decay for magnetohydrodynamic equations ⋮ Unique weak solutions of the magnetohydrodynamic equations with fractional dissipation ⋮ Sharp decay estimates for 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion ⋮ Stability of the 3D Boussinesq equations with partial dissipation near the hydrostatic balance ⋮ Stability and optimal decay for the 3D magnetohydrodynamic equations with only horizontal dissipation ⋮ Optimal decay rates for \(n\)-dimensional generalized magnetohydrodynamic equations ⋮ Stabilization of a Background Magnetic Field on a 2 Dimensional Magnetohydrodynamic Flow ⋮ Sharp time decay rates of H ¹ weak solutions for the 2D MHD equations with linear damping velocity ⋮ Unnamed Item ⋮ Smoothing and stabilization effects of magnetic field on electrically conducting fluids ⋮ Well-posedness for the generalized Navier-Stokes-Landau-Lifshitz equations ⋮ The 3D incompressible Hall magneto-hydrodynamics equations with partial hyperdissipation ⋮ Pointwise stability of shock wave for 2D anisotropic viscous conservation laws with large perturbation ⋮ 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
• Unnamed Item
• 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
• Limiting case for the regularity criterion to the 3-D magneto-hydrodynamics equations
• Global small solutions of 2-D incompressible MHD system
• Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
• Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
• A regularity criterion for the 2D MHD system with zero magnetic diffusivity
• BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
• On the well-posedness of the ideal MHD equations in the Triebel-Lizorkin spaces
• Local existence for the non-resistive MHD equations in Besov spaces
• Global solutions to the 2D viscous, non-resistive MHD system with large background magnetic field
• The Beale-Kato-Majda criterion for the 3D magneto-hydrodynamics equations
• Two regularity criteria for the 3D MHD equations
• Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
• Generalized MHD equations.
• A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation
• Global regularity and time decay for the 2D magnetohydrodynamic equations with fractional dissipation and partial magnetic diffusion
• 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
• Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
• Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion
• Global regularity for a slightly supercritical hyperdissipative Navier-Stokes system
• Lagrangian-Eulerian methods for uniqueness in hydrodynamic systems
• Global regularity of the logarithmically supercritical MHD system with zero diffusivity
• On axially symmetric incompressible magnetohydrodynamics in three dimensions
• Global regularity of 2D generalized MHD equations with magnetic diffusion
• Mathematical results related to a two-dimensional magneto-hydrodynamic equations
• On the global well-posedness of \(N\)-dimensional generalized MHD system in anisotropic spaces
• On the regularity of weak solutions to the magnetohydrodynamic equations
• Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equa\-tions
• Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation
• An Introduction to Magnetohydrodynamics
• The 2D magnetohydrodynamic equations with magnetic diffusion
• Magnetic Reconnection
• Global Well-posedness of two-dimensional Magnetohydrodynamic Flows with Partial Dissipation and Magnetic Diffusion
• Global Small Solution to the 2D MHD System with a Velocity Damping Term
• Global Small Solutions to Three-Dimensional Incompressible Magnetohydrodynamical System
• Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case
• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
• Regularity Criteria for the Generalized MHD Equations

This page was built for publication: The 3D incompressible magnetohydrodynamic equations with fractional partial dissipation