An Improved Result on Rayleigh--Taylor Instability of Nonhomogeneous Incompressible Viscous Flows

  title={An Improved Result on Rayleigh--Taylor Instability of Nonhomogeneous Incompressible Viscous Flows},
  author={Fei Jiang},
  journal={arXiv: Analysis of PDEs},
  • F. Jiang
  • Published 2 January 2015
  • Mathematics
  • arXiv: Analysis of PDEs
In [F. Jiang, S. Jiang, On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain, Adv. Math., 264 (2014) 831--863], Jiang investigated the instability of Rayleigh--Taylor steady-state of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain $\Omega$ of class $C^2$. In particular, they proved the steady-state is nonlinearly unstable under a restrictive condition of that the derivative function of… 
11 Citations

On Classical Solutions of Rayleigh--Taylor Instability in Inhomogeneous Incompressible Viscous Fluids in Bounded Domains

We study the existence of unstable classical solutions of the Rayleigh--Taylor instability problem (abbr. RT problem) of an inhomogeneous incompressible viscous fluid in a bounded domain. We find

On instability of Rayleigh–Taylor problem for incompressible liquid crystals under L 1 $L^{1}$ -norm

We investigate the nonlinear Rayleigh–Taylor (RT) instability of a nonhomogeneous incompressible nematic liquid crystal in the presence of a uniform gravitational field. We first analyze the

On the Rayleigh–Taylor instability in compressible viscoelastic fluids

Rayleigh–Taylor instability for nonhomogeneous incompressible fluids with Navier‐slip boundary conditions

This paper is concerned with the Rayleigh–Taylor instability for the nonhomogeneous incompressible Navier–Stokes equations with Navier‐slip boundary conditions around a steady state in an infinite

On effects of elasticity and magnetic fields in the linear Rayleigh–Taylor instability of stratified fluids

It is proved that there exists an unstable solution to the linearized stratified viscoelastic Rayleigh–Taylor problem with the largest growth rate as κ increases from 0 to κc$\kappa_{{c}}$.

On the stability of Rayleigh–Taylor problem for stratified rotating viscoelastic fluids

We investigate the stability of Rayleigh–Taylor (RT) problem of the stratified incompressible viscoelastic fluids under the rotation and the gravity in a horizontal periodic domain, in which the



Nonlinear instability for nonhomogeneous incompressible viscous fluids

We investigate the nonlinear instability of a smooth steady density profile solution to the three-dimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform

On the Rayleigh-Taylor Instability for Incompressible, Inviscid Magnetohydrodynamic Flows

This work studies the Rayleigh–Taylor instability for two incompressible, immiscible, inviscid magnetohydrodynamic (MHD) fluids with zero resistivity, evolving with a free interface in the presence of a uniform gravitational field, and constructs normal mode solutions to the linearized problem that grow exponentially in time.

Nonlinear Rayleigh-Taylor Instability for Nonhomogeneous Incompressible Viscous Magnetohydrodynamic Flows

We investigate the nonlinear instability of a smooth Rayleigh-Taylor steady-state solution (including the case of heavier density with increasing height) to the three-dimensional incompressible

Linear Rayleigh-Taylor Instability for Viscous, Compressible Fluids

This work develops a general method of studying a family of modified variational problems in order to produce maximal growing modes and proves an estimate for arbitrary solutions to the linearized equations in terms of the fastest possible growth rate for the growing modes.

On the Rayleigh–Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations

We study the Rayleigh-Taylor instability problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows with zero resistivity and surface tension (or without surface tension),

Compressible, inviscid Rayleigh-Taylor instability

We consider the Rayleigh-Taylor problem for two compressible, immiscible, inviscid, barotropic fluids evolving with a free interface in the presence of a uniform gravitational field. After

On the Rayleigh-Taylor Instability for the two-Phase Navier-Stokes Equations

The two-phase free boundary problem with surface tension and downforce gravity for the Navier-Stokes system is considered in a situation where the initial interface is close to equilibrium. The

The Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh–Taylor Instability

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally