Related papers: On the rigorous mathematical derivation for the vi…
In the mathematical modelling of compactional flow in porous media, the constitutive relation is typically modelled in terms of a nonlinear relationship between effective pressure and porosity, and compaction is essentially poroelastic.…
We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain.…
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term.…
In this paper, we prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the viscosity sense. The results cover the complex Hessian quotient…
We consider the one-dimensional Cauchy problem for the Navier-Stokes equations with degenerate viscosity coefficient in highly compressible regime. It corresponds to the compressible Navier-Stokes system with large Mach number equal to…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
By means of the Hamiltonian approach to two-dimensional wave motions in heterogeneous fluids proposed by Benjamin, we derive a natural Hamiltonian structure for ideal fluids, density stratified in four homogenous layers, constrained in a…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
A new mechanism of double-component convection is discovered. It emerges in a horizontal layer of Boussinesq fluid as a stable stratification due to flux boundary conditions is added to an unstable gradient specified by fixed boundary…
We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero…
We examine the translation of a sphere in a stably stratified ambient in the limit of small Reynolds ($Re \ll 1$) and viscous Richardson numbers ($Ri_v \ll 1$); here, $Re = \frac{\rho Ua}{\mu}$ and $Ri_v = \frac{\gamma a^3 g}{\mu U}$ with…
In this paper we study the zero-viscosity limit of $2$-D Boussinesq equations with vertical viscosity and zero diffusivity, which is a nonlinear system with partial dissipation arising in atmospheric sciences and oceanic circulation. The…
This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…
We consider the sedimentation of $N$ spherical particles with identical radii $R$ in a Stokes flow in $\mathbb R^3$. The particles satisfy a no-slip boundary condition and are subject to constant gravity. The dynamics of the particles is…
We derive a relationship for the vortex aspect ratio $\alpha$ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Vaisala frequencies…
The water wave theory traditionally assumes the fluid to be perfect, thus neglecting all effects of the viscosity. However, the explanation of several experimental data sets requires the explicit inclusion of dissipative effects. In order…
The sedimentation of a spherical particle in an elastoviscoplastic fluid in proximity of a flat wall is investigated by direct numerical simulations. The governing equations under inertialess conditions are solved by the finite element…
We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…
This paper considers a modular grad-div stabilization method for approximating solutions of the time-dependent Boussinesq model of non-isothermal flows. The proposed method adds a minimally intrusive step to an existing Boussinesq code,…
Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible…