Related papers: The $N$-dimensional gravity driven Muskat problem
We construct a duality manifest gravitational theory for the special linear group, ${\mathbf{SL}(N)}$ with $N{\neq 4}$. The spacetime is formally extended, to have the dimension $\textstyle{\frac{1}{2}} N(N-1)$, yet is `gauged'.…
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…
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 fluid is bounded above by a trivial fluid of constant…
We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a…
This paper studies the two-dimensional inhomogeneous Navier--Stokes equations governing stratified flows in a bounded domain under a gravitational potential \(f\). Our main results are as follows. First, we provide a rigorous…
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…
We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS)…
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, in the form of a new…
We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…
We prove the local existence of solutions of the form $x^2+ct+g,$ with $g\in H^s(\mathbb R)$ and $s\geq 3,$ for the Muskat problem in the stable regime. We use energy methods to obtain a bound of $g$ in Sobolev spaces. In the proof we deal…
This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations…
We study the Neumann and Dirichlet problems for the total variation flow in metric measure spaces. We prove existence and uniqueness of weak solutions and study their asymptotic behaviour. Furthermore, in the Neumann problem we provide a…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
In the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…
The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in…
We consider the gravitational clustering of a multicomponent fluid in an expanding Newtonian universe, taking into account the mutual gravitational interactions of the medium. We obtain a set of exact and approximate solutions for two fluid…
We show that the classification of shearless and incompressible stationary fluid flows on ultrastatic manifolds is equivalent to classifying the isometries of the spatial sections. For a flow on R x S$^2$ this leaves only one possibility,…