Related papers: An ill-posed problem in hydrodynamic stability of …
The primitive equations (PE) are a fundamental model in geophysical fluid dynamics. While the viscous PE are globally well-posed, their inviscid counterparts are known to be ill-posed. In this paper, we study the two-dimensional…
We study the Abels-Garcke-Gr\"un (AGG) model for a mixture of two viscous incompressible fluids with different densities. The AGG model consists of a Navier-Stokes-Cahn-Hilliard system characterized by a (non-constant)…
Polymer solutions are often injected in porous media for applications such as oil recovery and groundwater remediation. As the fluid navigates the tortuous pore space, elastic stresses build up, causing the flow to become unstable at…
Two dimensional free surface flows in Hele-Shaw configurations are a fertile ground for exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid--fluid interfaces, significant effort has been expended to…
The Hele-Shaw experiment is performed with a circular invasion to study the scaling and dynamic behavior of the interface. We did not find any universal power law. The time exponent varies with the range of scale, as has been reported in…
The displacement of multiphase fluid flow in a pore doublet is a fundamental problem, and is also of importance in understanding of the transport mechanisms of multiphase flows in the porous media. During the displacement of immiscible…
The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close…
The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer…
We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly-packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced…
Motivated by the analysis of the propagation of internal waves in a stratified ocean, we consider in this article the incompressible Euler equations with variable density in a flat strip, and we study the evolution of perturbations of the…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
In this work, we present the stability theory for inhomogeneous fluids subjected to standing acoustic fields. Starting from the first principles, the stability criterion is established for two fluids of different acoustic impedance…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a…
Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analysed. We derive the thin-film Ericksen-Leslie equations that govern…
When immiscible wetting and non-wetting fluids move in parallel in a porous medium, an instability may occur at sufficiently high capillary numbers so that interfaces between the fluids initially held in place by the porous medium are…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
The incompressible smoothed particle hydrodynamics method (ISPH) is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical…
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…
We study the two-phase, horizontally periodic, quasistationary Stokes flow in two dimensions driven by surface tension and gravity effects in the general context of fluids with (possibly) different viscosities and densities. The sharp…