Related papers: Continuum mechanics of media with inner structures
We employ Besov space techniques and the method of modulus of continuity to obtain the global well-posedness of the modified Porous Media Equation.
A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…
We derive a new set of kinematic equations for front motion in two-dimensional bistable media. The equations generalize the geometric approach by complementing the equation for the front curvature with an order parameter equation associated…
Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…
It is shown that invariants and relativistically invariant laws of conservation of physical quantities in Minkowski space follow from 4-tensors of the second rank, which are four-dimensional derivatives of 4-vectors, tensor products of…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
We study the equilibrium configurations of a possibly asymmetric fluid-structure-interaction problem. The fluid is confined in a bounded planar channel and is governed by the stationary Navier-Stokes equations with laminar inflow and…
We consider the motion of compressible Navier-Stokes fluids with the hard sphere pressure law around a rigid obstacle when the velocity and the density at infinity are non zero. This kind of pressure model is largely employed in various…
We propose a mathematical derivation of stochastic compressible Navier-Stokes equation. We consider many-particle systems with a Hamiltonian dynamics supplemented by a friction term and environmental noise. Both the interaction potential…
We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure…
This work is a continuation of the analysis first presented in Cheung & Zaki (2014). In that study, the combination matrix was introduced as a means to tractably handle the nonlinear terms in the spectral domain. In this work, a different…
We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density…
Being based on V. Konoplev's axiomatic approach to continuum mechanics, the paper broadens its frontiers in order to bring together continuum mechanics with classical mechanics in a new theory of mechanical systems. There are derived motion…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and…
In part I of this paper, I proposed a new set of equations, which I refer to as the M(D,{\eta})-formulation and which differs from the Navier-Stokes-Fourier description of fluid motion. Here, I use these equations to model several classic…
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
Physical vacuum is a special superfluid medium. Its motion is described by the Navier-Stokes equation having two slightly modified terms that relate to internal forces. They are the pressure gradient and the dissipation force because of…
We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure…
We prove the existence of recurrent or Poisson stable motions in the Navier-Stokes fluid system under recurrent or Poisson stable forcing, respectively. We use an approach based on nonautonomous dynamical systems ideas.