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

@article{Jiang2015AnIR, title={An Improved Result on Rayleigh--Taylor Instability of Nonhomogeneous Incompressible Viscous Flows}, author={Fei Jiang}, journal={arXiv: Analysis of PDEs}, year={2015} }

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 et.al. 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

- Mathematics
- 2019

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 the Rayleigh-Taylor instability in compressible viscoelastic fluids under L1-norm

- MathematicsJ. Comput. Appl. Math.
- 2021

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

- Mathematics
- 2021

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

- MathematicsJournal of Mathematical Analysis and Applications
- 2018

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

- MathematicsMathematical Methods in the Applied Sciences
- 2020

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…

### Nonlinear convective instability in the compressible magnetic convection problem without heat conductivity

- Mathematics, PhysicsJournal of Mathematical Analysis and Applications
- 2018

### Instability solutions for the Rayleigh–Taylor problem of non-homogeneous viscoelastic fluids in bounded domains

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

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

- MathematicsJournal of inequalities and applications
- 2018

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

- MathematicsBoundary Value Problems
- 2018

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…

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