Related papers: Surface tension stabilization of the Rayleigh-Tayl…
We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
We consider the motion of two superposed immiscible, viscous, incompressible, capillary fluids that are separated by a sharp interface which needs to be determined as part of the problem. Allowing for gravity to act on the fluids, we prove…
We consider the free-boundary motion of two perfect incompressible fluids with different densities $\rho_+$ and $\rho_-$, separated by a surface of discontinuity along which the pressure experiences a jump proportional to the mean curvature…
Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is shown that the resulting systems are thermodynamically…
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 nonhomogeneous magnetohydrodynamic (MHD)…
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…
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 boundary symbol of this problem admits zeros…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
We present the linear theory of two-dimensional incompressible magneto-Rayleigh-Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and…
We study the dynamics of the interface given by two incompressible viscous fluids in the Stokes regime filling a 2D horizontally periodic strip. The fluids are subject to the gravity force and the density difference induces the dynamics of…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
The Muskat problem, in its general setting, concerns the interface evolution between two incompressible fluids of different densities and viscosities in porous media. The interface motion is driven by gravity and capillarity forces, where…
We study the drainage of a viscous liquid film coating outside a horizontal cylinder. We first study the evolution of the axially invariant draining flow, initiated at rest with uniform film thickness $\delta$. Non-linear simulations…
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary…
Rayleigh-Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present linearized theory for arbitrary 3D initial disturbances that grow in time, and…
We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional MHD simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact…