Related papers: Large traveling capillary-gravity waves for Darcy …
We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given…
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…
We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The…
We introduce a two-dimensional Hele-Shaw type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion of the cytoskeleton gel (active gel) coupled with…
We consider one dimensional porous media equations in spatially periodic environment. We will construct a periodic traveling sharp wave whose profile tends to a positive steady state at left infinity and takes zero on the right half line,…
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force…
In this paper, we present a cell motility model that takes into account the cell membrane effect. The model introduced is an incompressible Darcy free boundary problem. This model involves a nonlinear term in the boundary condition to model…
We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can…
We find a new class of solutions that are traveling waves on the boundary of two--dimensional droplet of ideal fluid. We assume that the free surface is subject only to the force of surface tension, and the fluid flow is potential. We use…
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…
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…
In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the…
In this paper, we consider capillary-gravity waves propagating on the interface separating two fluids of finite depth and constant density. The flow in each layer is assumed to be incompressible and of constant vorticity. We prove the…
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions…
In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
The free boundary problem for a two-dimensional fluid filtered in porous media is studied. This is known as the one-phase Muskat problem and is mathematically equivalent to the vertical Hele-Shaw problem driven by gravity force. We prove…
In this paper, we prove the existence of two-dimensional, traveling, capillary-gravity, water waves with compactly supported vorticity. Specifically, we consider the cases where the vorticity is a $\delta$-function (a point vortex), or has…