Related papers: Large-amplitude internal fronts in two-fluid syste…
This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard's Semicircle Theorem and study the eigenvalue distribution of the linearized Euler…
This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…
Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus $\mathbb T^3$. The building blocks in their proof are Beltrami flows, which are inherently…
In this article we investigate the two-dimensional incompressible rotating and stratified, just rotating, just stratified Euler equations with each other and with the normal Euler equations with the self-similar Ansatz. There are analytic…
We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting in…
In this paper, we prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed…
We give the first mathematical construction of two-dimensional traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations for a single finite depth layer of constant density fluid. Our construction is based on…
We consider a two-phase problem for two incompressible, viscous and immiscible fluids which are separated by a sharp interface. The problem arises as a sharp interface limit of a diffuse interface model. We present results on local…
Tai-Ping Liu \cite{Liu\_JJ} introduced the notion of "physical solution' of the isentropic Euler system when the gas is surrounded by vacuum. This notion can be interpreted by saying that the front is driven by a force resulting from a…
We study the rate of growth of sharp fronts of the Quasi-geostrophic equation and 2D incompressible Euler equations.. The development of sharp fronts are due to a mechanism that piles up level sets very fast. Under a semi-uniform collapse,…
In this work, we study the behaviour of saturation fronts for two phase flow through a long homogeneous porous column. In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the…
This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the…
In this paper, a unified theory of internal bores and gravity currents is presented within the framework of the one-dimensional two-layer shallow-water equations. The equations represent four basic physical laws: the theory is developed on…
In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points…
In this article we consider the multi-layer shallow water system for the propagation of gravity waves in density-stratified flows, with additional terms introduced by the oceanographers Gent and McWilliams in order to take into account…
Analytic global bifurcation theory is used to construct a large variety of families of steady periodic two-dimensional gravity water waves with real-analytic vorticity distributions, propagating in an incompressible fluid. The waves that…
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in Lortz, they do possess a planar reflection symmetry and, as…
In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier--Stokes…
In this text, the filtering unitary group method developed, among others, by S. Schochet is adapted to prove the existence and well-posedness of modulation equations describing the incompressible limit of the Euler-Maxwell Two-Fluid (EMTF)…
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the…