On the Exponential Stability of a Stratified Flow to the 2D Ideal MHD Equations with Damping

DOI10.1137/18M1215931zbMath1431.35122arXiv1910.10598OpenAlexW2995726661WikidataQ115525588 ScholiaQ115525588MaRDI QIDQ5206160

Yi Zhou, Wang Yang, Yi Du

Publication date: 18 December 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.10598

zbMATH Keywords

exponential stabilitystratified flow2D ideal MHD equations with damping

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Magnetohydrodynamics and electrohydrodynamics (76W05) Stability and instability of magnetohydrodynamic and electrohydrodynamic flows (76E25) Initial value problems for first-order hyperbolic systems (35L45) Stratification effects in inviscid fluids (76B70)

Related Items (7)

Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping ⋮ Global Solutions of the Three-Dimensional Incompressible Ideal MHD Equations with Velocity Damping in Horizontally Periodic Domains ⋮ On magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids: global existence of large solutions ⋮ A regularity criterion for the 3D generalized MHD system involving partial components ⋮ On echoes in magnetohydrodynamics with magnetic dissipation ⋮ Asymptotic behaviors of global solutions to the two-dimensional non-resistive MHD equations with large initial perturbations ⋮ On inhibition of the Rayleigh-Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping

Cites Work

• Unnamed Item
• Asymptotic behavior of solutions of the compressible Navier-Stokes equation around the plane Couette flow
• On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain
• Global small solutions of 2-D incompressible MHD system
• On the stability threshold for the 3D Couette flow in Sobolev regularity
• 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
• Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
• Stability of plane Couette flows with respect to small periodic perturbations
• Global classical solutions of three dimensional viscous MHD system without magnetic diffusion on periodic boxes
• Stability of plane-parallel Couette flow
• Almost exponential decay of periodic viscous surface waves without surface tension
• Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion
• Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow
• Global small solutions to a complex fluid model in three dimensional
• Instability of plane Poiseuille flow in viscous compressible gas
• Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid
• Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation
• An Introduction to Magnetohydrodynamics
• Linear Rayleigh–Taylor Instability for Viscous, Compressible Fluids
• Some mathematical questions related to the mhd equations
• Longtime Dynamics of a Conductive Fluid in the Presence of a Strong Magnetic Field
• Global classical solutions of 2D MHD system with only magnetic diffusion on periodic domain
• On the Stabilizing Effect of the Magnetic Fields in the Magnetic Rayleigh--Taylor Problem
• Hydrodynamic Stability
• Instability of periodic BGK equilibria
• On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term
• Global Small Solution to the 2D MHD System with a Velocity Damping Term

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