On linear instability and stability of the Rayleigh-Taylor problem in magnetohydrodynamics

DOI10.1007/s00021-015-0221-xzbMath1327.76074arXiv1504.06912OpenAlexW3099941921MaRDI QIDQ889648

Song Jiang, Fei Jiang

Publication date: 9 November 2015

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.06912

zbMATH Keywords

equilibrium statesincompressible/compressible fluidsinstability/stability criteriamagnetic Rayleigh-Taylor instabilityparker's instabilityviscous MHD equations

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Stability and instability of magnetohydrodynamic and electrohydrodynamic flows (76E25)

Related Items (43)

On exponential stability of gravity driven viscoelastic flows ⋮ On effects of elasticity and magnetic fields in the linear Rayleigh-Taylor instability of stratified fluids ⋮ On the stability of Rayleigh-Taylor problem for stratified rotating viscoelastic fluids ⋮ On instability of Rayleigh-Taylor problem for incompressible liquid crystals under \(L^1\)-norm ⋮ Renormalized weak solutions to the three-dimensional steady compressible magnetohydrodynamic equations ⋮ Instability solutions for the Rayleigh-Taylor problem of non-homogeneous viscoelastic fluids in bounded domains ⋮ On the Rayleigh-Taylor instability for the compressible non-isentropic inviscid fluids with a free interface ⋮ Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions ⋮ On Rayleigh-Taylor instability in nonhomogeneous incompressible elasticity fluids ⋮ On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping ⋮ Nonlinear convective instability in the compressible magnetic convection problem without heat conductivity ⋮ Time-decay solutions of the initial-boundary value problem of rotating magnetohydrodynamic fluids ⋮ The Rayleigh-Taylor instability of incompressible Euler equations in a horizontal slab domain ⋮ Rayleigh-Taylor instability for incompressible viscous quantum flows ⋮ On magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids: global existence of large solutions ⋮ On the dynamic Rayleigh-Taylor instability in the Euler-Korteweg model ⋮ 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 ⋮ Stabilizing Effect of Capillarity in the Rayleigh–Taylor Problem to the Viscous Incompressible Capillary Fluids ⋮ The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time‐decay rates ⋮ Nonlinear stability of the viscoelastic Bénard problem ⋮ On Rayleigh-Taylor instability in Navier-Stokes-Korteweg equations ⋮ On the Rayleigh-Taylor instability in compressible viscoelastic fluids under \(L^1\)-norm ⋮ On the Stabilizing Effect of the Magnetic Fields in the Magnetic Rayleigh--Taylor Problem ⋮ On the dynamic instability of non‐Newtonian fluids driven by gravity ⋮ Stability of the viscoelastic Rayleigh-Taylor problem with internal surface tension ⋮ Sharp nonlinear stability criterion of viscous non-resistive MHD internal waves in 3D ⋮ On the dynamical stability and instability of parker problem ⋮ On Parker instability under \(L^2\)-norm ⋮ On the Rayleigh-Taylor instability in compressible viscoelastic fluids ⋮ Nonlinear stability and instability in the Rayleigh-Taylor problem of stratified compressible MHD fluids ⋮ On the nonlinear Rayleigh-Taylor instability of nonhomogeneous incompressible viscoelastic fluids under \(L^{2}\)-norm ⋮ Decay-in-time of the highest-order derivatives of solutions for the compressible isentropic MHD equations ⋮ Stabilizing effect of elasticity on the motion of viscoelastic/elastic fluids ⋮ Instability of the abstract Rayleigh–Taylor problem and applications ⋮ On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability ⋮ A new upper bound for the largest growth rate of linear Rayleigh-Taylor instability ⋮ On inhibition of the Rayleigh-Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping ⋮ 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 ⋮ On classical solutions of Rayleigh-Taylor instability in inhomogeneous viscoelastic fluids ⋮ On effect of surface tension in the Rayleigh-Taylor problem of stratified viscoelastic fluids

Cites Work

• Nonlinear instability for nonhomogeneous incompressible viscous fluids
• On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain
• Nonlinear instability for the critically dissipative quasi-geostrophic equation
• Nonlinear Rayleigh-Taylor instability for nonhomogeneous incompressible viscous magnetohydrodynamic flows
• Nonlinear instability in an ideal fluid
• On the dynamical Rayleigh-Taylor instability
• Nonlinear instability in two-dimensional ideal fluids: the case of a dominant eigenvalue
• Elliptic partial differential equations of second order
• Unique solvability for the density-dependent Navier-Stokes equations
• Nonlinear instability of double-humped equilibria
• Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
• Critical magnetic number in the magnetohydrodynamic Rayleigh-Taylor instability
• Compressible, inviscid Rayleigh-Taylor instability
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• Linear Rayleigh–Taylor Instability for Viscous, Compressible Fluids
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Waves a heavy, viscous, incompressible, electrically conducting fluid of variable density, in the presence of a magnetic field
• Variational approach to nonlinear gravity-driven instabilities in a MHD setting
• Classical Fourier Analysis
• Instability of periodic BGK equilibria
• On the Rayleigh–Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations
• Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case
• Some instabilities of a completely ionized plasma
• Unnamed Item
• Unnamed Item

This page was built for publication: On linear instability and stability of the Rayleigh-Taylor problem in magnetohydrodynamics