Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

We investigate the incompressible Navier–Stokes equations with variable density. The aim
is to prove existence and uniqueness results in the case of discontinuous initial density. In …

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

Based on a bootstrap instability method, we prove the existence of unstable strong solutions
in the sense of L 1-norm to an abstract Rayleigh–Taylor (RT) problem arising from stratified …

We investigate the instability and stability of some steady-states of a three-dimensional
nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain Ω of …

We consider the dynamics of two layers of incompressible electrically conducting fluid
interacting with a magnetic field, which are confined within a 3D horizontally infinite slab and …

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid
lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper …

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 …

This paper is concerned with the instability and stability of the trivial steady states of the
incompressible Navier–Stokes equations with Navier-slip boundary conditions in a slab …

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid
lying atop one another. The lower fluid is bounded below by a rigid bottom, and t he upper …