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Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized Navier--Stokes equations and convection - diffusion equation with diffusivity dependent on the…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
The aim of this paper is to study the stability of soliton-like static solutions via non-linear simulations in the context of a special class of massive tensor-multi-scalar-theories of gravity whose target space metric admits Killing…
In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
This paper analyzes rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-$C^0$ rectangular Morley element is uniformly convergent in the energy norm with respect to the…
First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime.…
The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…
We describe conformal field theories, correlation functions of which satisfy equations of the two-dimensional fluid mechanics. Prediction for the energy spectrum is given, $E(k) \sim k^{-25/7}$.
We introduce a new computationally efficient and accurate classical density-functional theory for water and apply it to hydration of hard spheres and inert gas atoms. We find good agreement with molecular dynamics simulations for the…
We study a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. Global existence,…
The completeness of solutions of homogeneous as well as non-homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
A criterion is presented and discussed to detect when a divergence-free perfect fluid energy tensor in the space-time describes an evolution in local thermal equilibrium. This criterion is applied to the class II Szafron-Szekeres perfect…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
A series of experiments for steady state rotation of water in vessels of various geometries is presented. The experiments focus on the geometrical characteristics of the rotating liquids and the change in their surface topology, from that…
We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides…