相关论文: Energy dissipation and self-similar solutions for …

The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order…

Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…

In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…

This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…

A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities…

We consider shell models that display an inverse energy cascade similar to 2-dimensional turbulence (together with a direct cascade of an enstrophy-like invariant). Previous attempts to construct such models ended negatively, stating that…

We derive statistical equilibrium solutions of the truncated inviscid surface quasi-geostrophic (SQG) equations, and verify the validity of these solutions at late times in numerical simulations of the truncated SQG equations. The results…

In this paper we concern ourselves with an incompressible, viscous, isotropic, and periodic micropolar fluid. We find that in the absence of forcing and microtorquing there exists an infinite family of well-behaved solutions, which we call…

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…

We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a…

A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent…

Energy dissipation in sheared dry and wet granulates is considered in the presence of an externally applied confining pressure. Discrete element simulations reveal that for sufficiently small confining pressures, the energy dissipation is…

We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. The underlying relative energy inequality holds as an equality for classical solutions and if the additional variable vanishes, these…

Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…

We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force,…

We consider a viscous incompressible fluid below the air and above a fixed bottom. The fluid dynamics is governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free…

In Part I of this paper series, a theoretical and numerical model for a a driven pendulum filled with liquid was developed. The system was analyzed in the framework of tuned liquid dampers (TLD) and hybrid mass liquid dampers (HMLD) theory.…

We consider a coupled system of partial and ordinary differential equations describing the interaction between an isentropic inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions…

Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique…

In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a…