Related papers: Conserved quantities and regularity in fluid dynam…
The paper deals with the problem of the energy conservation for the weak solutions to the compressible Primitive Equations (CPE) system with degenerate viscosity. The sufficient conditions on the regularity of weak solutions for the energy…
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…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
We give a localized regularity condition for energy conservation of weak solutions of the Euler equations on a domain $\Omega\subset \mathbb{R}^d$, $d\ge 2$, with boundary. In the bulk of fluid, we assume Besov regularity of the velocity…
This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…
We formulate a thermodynamically consistent continuum theory for compressible, viscous, heat-conducting fluids in which the velocity entering the balance of mass is distinguished from the specific linear momentum entering the balances of…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
Incompressible fluid equations are studied with UV cut-off and in periodic boundary conditions. Properties of the resulting ODEs holding uniformly in the cut-off are considered and, in particular, are conjectured to be equivalent to…
At the molecular level fluid motions are, by first principles, described by time reversible laws. On the other hand, the coarse grained macroscopic evolution is suitably described by the Navier-Stokes equations, which are inherently…
From a simple analysis of particle orbits and fluid flows in presence or not of dissipation, some connections between apparently uncorrelated research areas are made. The main results point out for a deep relation between quantization of…
Understanding complexity in fluid mechanics is a major problem that has attracted the attention of physicists and mathematicians during the last decades. Using the concept of renormalization in dynamics, we show the existence of a locally…
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…
We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in…
Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for…
We investigate divergence-type theories (DTT) describing the dissipative interaction between a field and a fluid. We look for theories which, under equilibrium conditions, reduce to the theory of a Klein-Gordon scalar field and a perfect…
We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon…
In this paper the author considers the motion of a relativistic perfect fluid with self-interaction mediated by Nordstrom's scalar theory of gravity. The evolution of the fluid is determined by a quasilinear hyperbolic system of PDEs, and a…
We study conservation properties of Galerkin methods for the incompressible Navier-Stokes equations, without the divergence constraint strongly enforced. In typical discretizations such as the mixed finite element method, the conservation…
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…
We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical…