Global small solutions of 2-D incompressible MHD system

From MaRDI portal

Publication:491906

Jump to:navigation, search

DOI10.1016/j.jde.2015.06.034zbMath1321.35138arXiv1302.5877OpenAlexW2964305021MaRDI QIDQ491906

Li Xu, Ping Zhang, Fang-Hua Lin

Publication date: 19 August 2015

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

Full work available at URL: https://arxiv.org/abs/1302.5877

zbMATH Keywords

Lagrangian coordinates anisotropic Littlewood-Paley theory dissipative estimates inviscid MHD system

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Navier-Stokes equations (35Q30) A priori estimates in context of PDEs (35B45) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items

Asymptotic stability of the 2D MHD equations without magnetic diffusion ⋮ Asymptotic stability of the 2D MHD equations without resistivity on a flat strip domain ⋮ Stability for the 2D MHD equations with horizontal dissipation ⋮ Global Well-Posedness of the 2D MHD Equations of Damped Wave Type in Sobolev Space ⋮ Global existence and uniqueness theorem to 2-D incompressible non-resistive MHD system with non-equilibrium background magnetic field ⋮ Uniform regularity estimates and inviscid limit for the compressible non-resistive magnetohydrodynamics system ⋮ The 2D magnetohydrodynamic equations with magnetic diffusion ⋮ Global existence of three dimensional incompressible MHD flows ⋮ The inviscid limit for the incompressible stationary magnetohydrodynamics equations in three dimensions ⋮ Optimal error estimates of a Crank–Nicolson finite element projection method for magnetohydrodynamic equations ⋮ Global Existence and Time-decay Rates of Solutions to 2D Magneto-micropolar Fluid Equations with Partial Viscosity ⋮ On the rigidity from infinity for nonlinear Alfvén waves ⋮ Global Well-Posedness of the Inviscid Heat-Conductive Resistive Compressible MHD in a Strip Domain ⋮ Global classical solutions of 2D MHD system with only magnetic diffusion on periodic domain ⋮ Global smooth solutions to the 3D generalized Hall-magnetohydrodynamic equations with large data ⋮ Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction ⋮ On the temporal decay for the 2D non-resistive incompressible MHD equations ⋮ Global Solutions of the Three-Dimensional Incompressible Ideal MHD Equations with Velocity Damping in Horizontally Periodic Domains ⋮ Vanishing dissipation limit of solutions to initial boundary value problem for three dimensional incompressible magneto-hydrodynamic equations with transverse magnetic field ⋮ Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn-Hilliard-magnetohydrodynamics system of equations ⋮ Stabilization effects of magnetic field on a 2D anisotropic MHD system with partial dissipation ⋮ On the large data global well-posedness of inviscid axially symmetric MHD-Boussinesq system ⋮ Mild Ill-Posedness for 2D Magneto-Micropolar Fluid Equations Near a Background Magnetic Field ⋮ Stability of 2D inviscid MHD equations with only vertical magnetic diffusion on T2 ⋮ Global small solutions to the 3D compressible viscous non-resistive MHD system ⋮ Block preconditioners for energy stable schemes of magnetohydrodynamics equations ⋮ Global well‐posedness for the three‐dimensional incompressible viscous nonresistive magnetohydrodynamics equations in an infinite slab ⋮ Global Solutions to 3D Incompressible MHD System with Dissipation in Only One Direction ⋮ On magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids: global existence of large solutions ⋮ A second-order scheme based on blended BDF for the incompressible MHD system ⋮ 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 ⋮ Global solutions to the damped MHD system ⋮ Stability for the 2D incompressible MHD equations with only magnetic diffusion ⋮ Global regularity of 2D incompressible magneto-micropolar fluid equations with partial viscosity ⋮ 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 ⋮ Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations ⋮ On the blow-up criterion for the Hall-MHD problem with partial dissipation in \(\mathbb{R}^3\) ⋮ Global smooth solutions to the 3D compressible viscous non-isentropic magnetohydrodynamic flows without magnetic diffusion ⋮ Stability and exponential decay for magnetohydrodynamic equations ⋮ Global well-posedness and decay of the 2D incompressible MHD equations with horizontal magnetic diffusion ⋮ Stability near hydrostatic equilibrium to the three-dimensional magnetic Bénard fluid equations with partial dissipation ⋮ Stability and decay estimates of the 2D incompressible magneto-micropolar fluid system with partial viscosity on a flat Strip ⋮ Stability and optimal decay for the 3D magnetohydrodynamic equations with only horizontal dissipation ⋮ Optimal decay rates for \(n\)-dimensional generalized magnetohydrodynamic equations ⋮ Asymptotic stability and large time behavior of some three dimension magnetohydrodynamic equations ⋮ Large time behavior of the solutions to 3D incompressible MHD system with horizontal dissipation or horizontal magnetic diffusion ⋮ Sharp ill-posedness for the non-resistive MHD equations in Sobolev spaces ⋮ Global Well-Posedness of an Initial-Boundary Value Problem for Viscous Non-Resistive MHD Systems ⋮ Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative ⋮ On classical solutions to the Cauchy problem of the 2D compressible non-resistive MHD equations with vacuum states ⋮ Determining modes and determining nodes for the 3D non-autonomous regularized magnetohydrodynamics equations ⋮ Stability of the 3D incompressible Navier-Stokes equations with fractional horizontal dissipation ⋮ On the global solvability and the non-resistive limit of the one-dimensional compressible heat-conductive MHD equations ⋮ Stabilization of a Background Magnetic Field on a 2 Dimensional Magnetohydrodynamic Flow ⋮ Unnamed Item ⋮ On the steady Prandtl type equations with magnetic effects arising from 2D incompressible MHD equations in a half plane ⋮ Stabilizing Phenomenon for 2D Anisotropic Magnetohydrodynamic System near a Background Magnetic Field ⋮ Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model ⋮ Asymptotic stability of equilibrium to 3-D MHD system ⋮ On the Exponential Stability of a Stratified Flow to the 2D Ideal MHD Equations with Damping ⋮ On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids ⋮ On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term ⋮ Well-posedness for compressible MHD systems with highly oscillating initial data ⋮ Global regularity to the 3D MHD equations with large initial data in bounded domains ⋮ On the Global Solution of a 3‐D MHD System with Initial Data near Equilibrium ⋮ Global weak solutions and long time behavior for 1D compressible MHD equations without resistivity ⋮ Justification of Prandtl Ansatz for MHD Boundary Layer ⋮ Influence of a background magnetic field on a 2D magnetohydrodynamic flow ⋮ Unnamed Item ⋮ On Global-in-Time Weak Solutions to a Two-Dimensional Full Compressible NonResistive MHD System ⋮ Global Regularity for the 2D MHD Equations with Partial Hyper-resistivity ⋮ Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov-Sobolev-type spaces ⋮ Global well-posedness of the MHD equations in a homogeneous magnetic field ⋮ Global well-posedness of the MHD equations via the comparison principle ⋮ On 2-D Boussinesq equations for MHD convection with stratification effects ⋮ One component regularity criteria for the axially symmetric MHD-Boussinesq system ⋮ Well-posedness for the three dimension magnetohydrodynamic system in the anisotropic Besov spaces ⋮ Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping ⋮ On regularity criteria for the 2D generalized MHD system ⋮ Convergence analysis of an unconditionally energy stable projection scheme for magneto-hydrodynamic equations ⋮ Finite time singularity of the nematic liquid crystal flow in dimension three ⋮ Stability of the 3D incompressible MHD equations with horizontal dissipation in periodic domain ⋮ Second order unconditionally convergent and energy stable linearized scheme for MHD equations ⋮ Global well-posedness of 3d axisymmetric MHD-Boussinesq system with nonzero swirl ⋮ On the global well-posedness to the 3-D incompressible anisotropic magnetohydrodynamics equations ⋮ On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation ⋮ Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data ⋮ Global well-posedness for 2D non-resistive compressible MHD system in periodic domain ⋮ A stability problem for the 3D magnetohydrodynamic equations near equilibrium ⋮ An optimal error estimate of the BDF-Galerkin FEM for the incompressible MHD system ⋮ Global existence and decay of smooth solutions for the 3-D MHD-type equations without magnetic diffusion ⋮ Global well-posedness of 2D incompressible magnetohydrodynamic equations with horizontal dissipation ⋮ On global dynamics of three dimensional magnetohydrodynamics: nonlinear stability of Alfvén waves ⋮ Stability of perturbations near a background magnetic field of the 2D incompressible MHD equations with mixed partial dissipation ⋮ Remark on the global regularity of 2D MHD equations with almost Laplacian magnetic diffusion ⋮ Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects ⋮ Uniformly robust preconditioners for incompressible MHD system ⋮ On magnetic inhibition theory in non-resistive magnetohydrodynamic fluids ⋮ Global weak solutions to a two-dimensional compressible MHD equations of viscous non-resistive fluids ⋮ Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation ⋮ Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion ⋮ On inhibition of thermal convection instability by a magnetic field under zero resistivity ⋮ Mild solutions of the stochastic MHD equations driven by fractional Brownian motions ⋮ Global well-posedness for the 2D incompressible magneto-micropolar fluid system with partial viscosity ⋮ A class of large solutions to the 3D incompressible MHD and Euler equations with damping ⋮ Global regularity of 2D almost resistive MHD equations ⋮ Global classical solutions of three dimensional viscous MHD system without magnetic diffusion on periodic boxes ⋮ Uniform global solutions of the 3D compressible MHD system in a bounded domain ⋮ Global solutions to the 2D viscous, non-resistive MHD system with large background magnetic field ⋮ Global wellposedness of magnetohydrodynamics for Boussinesq system with partial viscosity and zero magnetic diffusion ⋮ On the dynamical stability and instability of parker problem ⋮ 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 ⋮ Stability of hydrostatic equilibrium for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity ⋮ Low regularity well-posedness for the 3D viscous non-resistive MHD system with internal surface wave ⋮ Global small finite energy solutions for the incompressible magnetohydrodynamics equations in \(\mathbb{R}^+ \times \mathbb{R}^2\) ⋮ Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density ⋮ Stabilized discontinuous Galerkin scheme for the magnetic induction equation ⋮ Large time behavior of solutions to 3-D MHD system with initial data near equilibrium ⋮ Global regularity of the 2D magnetohydrodynamic equations with fractional anisotropic dissipation ⋮ Stability of axially-symmetric solutions to incompressible magnetohydrodynamics with no azimuthal velocity and with only azimuthal magnetic field ⋮ Global well-posedness for the 2D non-resistive MHD equations in two kinds of periodic domains ⋮ Large time behavior of strong solutions to the 1D non-resistive full compressible MHD system with large initial data ⋮ Stability for a system of the 2D magnetohydrodynamic equations with partial dissipation ⋮ Critical conditions on \(w^\theta\) imply the regularity of axially symmetric MHD-Boussinesq systems ⋮ Local 4/5-law and energy dissipation anomaly in turbulence of incompressible MHD equations ⋮ Global well-posedness to the one-dimensional model for planar non-resistive magnetohydrodynamics with large data and vacuum ⋮ Asymptotic stability and decay rates for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity ⋮ Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces ⋮ Global solutions for the 3-D incompressible nonhomogeneous MHD equations ⋮ Global well-posedness of the incompressible magnetohydrodynamics ⋮ The 3D incompressible magnetohydrodynamic equations with fractional partial dissipation ⋮ Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusion ⋮ On the local \(C^{1,\alpha}\) solution of ideal magneto-hydrodynamical equations ⋮ Global regularity and time decay for the 2D magnetohydrodynamic equations with fractional dissipation and partial magnetic diffusion ⋮ Global strong solutions to the 3D incompressible MHD equations with density-dependent viscosity ⋮ Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion ⋮ Global well-posedness of 3D magneto-micropolar fluid equations with mixed partial viscosity near an equilibrium ⋮ Global strong solutions to the one-dimensional heat-conductive model for planar non-resistive magnetohydrodynamics with large data ⋮ Global well-posedness and analyticity for the 3D fractional magnetohydrodynamics equations in variable Fourier-Besov spaces ⋮ The resistive magnetohydrodynamic equation near an equilibrium ⋮ Initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection ⋮ Global weak solutions to a 2D compressible non-resistivity MHD system with non-monotone pressure law and nonconstant viscosity ⋮ Note on global regularity of 2D regularized MHD equations with zero magnetic diffusion ⋮ Global well-posedness for the 3D incompressible inhomogeneous Navier-Stokes equations and MHD equations ⋮ On the asymptotic stability of a stratified flow of the 2D non-resistive incompressible MHD equations ⋮ Global regularity for the \(2\frac{1}{2}\)D incompressible Hall-MHD system with partial dissipation ⋮ Global smooth solutions of the generalized MHD equations with large initial data ⋮ Global smooth axisymmetic solutions of the Boussinesq equations for magnetohydrodynamics convection ⋮ Global regularity of 2D generalized MHD equations with magnetic damping ⋮ A decoupled, linear and unconditionally energy stable scheme with finite element discretizations for magneto-hydrodynamic equations ⋮ Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations ⋮ Global regularity of 2D temperature-dependent MHD-Boussinesq equations with zero thermal diffusivity ⋮ Global regularity for the 2D MHD and tropical climate model with horizontal dissipation ⋮ Asymptotic behaviors of global solutions to the two-dimensional non-resistive MHD equations with large initial perturbations ⋮ On the ideal magnetohydrodynamics in three-dimensional thin domains: well-posedness and asymptotics ⋮ Global well-posedness for the density-dependent incompressible magnetohydrodynamic flows in bounded domains ⋮ Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations ⋮ Global stability solution of the 2D MHD equations with mixed partial dissipation ⋮ Global well-posedness for the 3-D MHD equations with partial diffusion in the periodic domain ⋮ Global well-posedness for the non-viscous MHD equations with magnetic diffusion in critical Besov spaces ⋮ Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces ⋮ Uniform regularity and vanishing viscosity limit for the incompressible non-resistive MHD system with TMF ⋮ Global weak solutions for the Cauchy problem to one-dimensional heat-conductive MHD equations of viscous non-resistive gas ⋮ Well-posedness, analyticity and time decay of the 3D fractional magneto-hydrodynamics equations in critical Fourier-Besov-Morrey spaces with variable exponent ⋮ Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the \(L^p\) framework ⋮ Global well-posedness for the compressible non-resistive MHD equations in a 3D infinite slab ⋮ On axially symmetric incompressible magnetohydrodynamics in three dimensions ⋮ On Moffatt's magnetic relaxation equations ⋮ Global well-posedness for the three-dimensional full compressible viscous non-resistive MHD system ⋮ Global regularity of the 2D generalized MHD equations with velocity damping and Laplacian magnetic diffusion

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:491906&oldid=12371474"