Asymptotic behaviors of global solutions to the two-dimensional non-resistive MHD equations with large initial perturbations

DOI10.1016/j.aim.2021.108084zbMath1479.35668arXiv2102.06861OpenAlexW3212013965MaRDI QIDQ2054255

Fei Jiang, Song Jiang

Publication date: 1 December 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.06861

zbMATH Keywords

dampingexponential time-decayalgebraic time-decaydecay in the field strengthincompressible MHD fluidsviscosity vanishing limit

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Periodic solutions to PDEs (35B10) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Perturbations in context of PDEs (35B20) Stability and instability of magnetohydrodynamic and electrohydrodynamic flows (76E25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

Related Items (13)

Asymptotic stability of the 2D MHD equations without magnetic diffusion ⋮ Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping ⋮ On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping ⋮ Global well-posedness and time-decay for the full compressible non-resistive MHD equations in a 3D infinite slab ⋮ Global Solutions of the Three-Dimensional Incompressible Ideal MHD Equations with Velocity Damping in Horizontally Periodic Domains ⋮ Global well‐posedness for the three‐dimensional incompressible viscous nonresistive magnetohydrodynamics equations in an infinite slab ⋮ On magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids: global existence of large solutions ⋮ The optimal temporal decay rates for compressible Hall-magnetohydrodynamics system ⋮ Stability near hydrostatic equilibrium to the three-dimensional magnetic Bénard fluid equations with partial dissipation ⋮ Asymptotic stability and large time behavior of some three dimension magnetohydrodynamic equations ⋮ Stability and exponential decay of the magnetic Bénard system with horizontal dissipation ⋮ Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations ⋮ Global well-posedness for the compressible non-resistive MHD equations in a 3D infinite slab

Cites Work

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• Local well-posedness of the viscous surface wave problem without surface tension
• Global small solutions of 2-D incompressible MHD system
• Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
• Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusion
• 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
• On global dynamics of three dimensional magnetohydrodynamics: nonlinear stability of Alfvén waves
• Global classical solutions of three dimensional viscous MHD system without magnetic diffusion on periodic boxes
• Sharp nonlinear stability criterion of viscous non-resistive MHD internal waves in 3D
• Large time behavior of solutions to 3-D MHD system with initial data near equilibrium
• Global well-posedness of the incompressible magnetohydrodynamics
• Global solution and large-time behavior of the \(3D\) compressible Euler equations with damping
• On inhibition of thermal convection instability by a magnetic field under zero resistivity
• On the dynamical stability and instability of parker problem
• 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
• The 3D compressible Euler equations with damping in a bounded domain
• 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 well-posedness for the 2D MHD equations without magnetic diffusion in a strip domain
• LOCAL STRONG SOLUTION TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC FLOW WITH LARGE DATA
• Instability of the abstract Rayleigh–Taylor problem and applications
• Longtime Dynamics of a Conductive Fluid in the Presence of a Strong Magnetic Field
• Global Well-Posedness of an Initial-Boundary Value Problem for Viscous Non-Resistive MHD Systems
• Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping
• Convergence rate estimates for the low Mach and Alfvén number three-scale singular limit of compressible ideal magnetohydrodynamics
• On the Global Solution of a 3‐D MHD System with Initial Data near Equilibrium
• On the Exponential Stability of a Stratified Flow to the 2D Ideal MHD Equations with Damping
• Global Small Solution to the 2D MHD System with a Velocity Damping Term
• Global Small Solutions to Three-Dimensional Incompressible Magnetohydrodynamical System
• OPTIMAL CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH POTENTIAL FORCES
• The pointwise estimates of solutions for Euler equations with damping in multi-dimensions

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