Related papers: Global Regularity for Gravity Unstable Muskat Bubb…
Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the…
We consider the mixed formulation of the equations governing Darcy-Forchheimer flow in porous media. We prove existence and uniqueness of a solution for the stationary problem and the existence of a solution for the transient problem.
Fragmentation of rotating gaseous systems via gravitational instability is believed to be a crucial mechanism in several astrophysical processes, such as formation of planets in protostellar discs, of molecular clouds in galactic discs, and…
The diffusion-driven growth of a dense cloud of bubbles immersed in a gas-supersaturated liquid is a problem that finds applications in several modern technologies such as solvent-exchange micro-reactors, nanotechnology or the manufacturing…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
We consider the free boundary problem for a layer of compressible viscous barotropic fluid lying above a fixed rigid bottom and below the atmosphere of positive constant pressure. The fluid dynamics is governed by the compressible…
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette…
Objects subjected to a constant force generally increase their velocity over time. This expectation fails whenever their energy is a smooth and periodic function of momentum, resulting in periodic Bloch oscillations instead. Periodic…
We demonstrate that emulsion droplets stabilized by interfacial particles become unstable beyond a size threshold set by gravity. This holds not only for colloids but supra-colloidal glass beads, using which we directly observe the ejection…
Molecular gas disks are generally Toomre stable ($Q_T>$1) and yet clearly gravitationally unstable to structure formation as evidenced by the existence of molecular clouds and ongoing star formation. This paper adopts a 3D perspective to…
We establish the existence of global weak solution in 2D and 3D, as well as the uniqueness of weak solution in 2D, for the Darcy-Boussinesq model for convection in layered porous media with square integrable initial data. We also derived…
A rigid body, with an interior cavity entirely filled with a Navier-Stokes liquid, moves in absence of external torques relative to the center of mass of the coupled system body-liquid (inertial motions). The only steady-state motions…
This paper is a continuation of the works in \cite{Euler} and \cite{NS}, where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively.…
We investigate the realization of non-singular bouncing cosmologies driven by causal bulk-viscous fluids within General Relativity, $f(R)$ gravity, and Loop Quantum Cosmology. Building on the no-go result of Eckart theory in spatially flat…
This paper investigates the Cauchy problem for the compressible pressureless Navier-Stokes system in $\mathbb{R}^d$ with $d \geq 2$. Unlike the standard isentropic compressible Navier-Stokes system, the density in the pressureless model…
We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear…
This paper reviews the essential physics of gravitational instability in a Robertson-Walker background spacetime. Three approaches are presented in a pedagogical manner, based on (1) the Eulerian fluid equations, (2) the Lagrangian…
We present a discussion of the effects induced by bulk viscosity either on the very early Universe stability and on the dynamics associated to the extreme gravitational collapse of a gas cloud. In both cases the viscosity coefficient is…
The diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable density stratification evolves. In an inclined porous medium,…