Related papers: On Scaling Solutions with a Dissipative Fluid
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We investigate the cosmological applications of fluids having an equation of state which is the analog to the one related to the isotropic deformation of crystalline solids, that is containing logarithmic terms of the energy density,…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…
We prove that the two fluid Landau hydrodynamic equations, when applied to a gas interacting with infinite scattering length (unitary gas) in the presence of harmonic trapping, admit exact scaling solutions of mixed compressional and…
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
We identify a class maximal dissipative solutions to models of compressible viscous fluids that maximize the energy dissipation rate. Then we show that any maximal dissipative solution approaches an equilibrium state for large times.
We study the asymptotic behaviour near extinction of positive solutions of the Cauchy problem for the fast diffusion equation with a subcritical exponent. We show that separable solutions are stable in some suitable sense by finding a class…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general…
We examine the dynamical implications of an interaction between some of the fluid components of the universe. We consider the combination of three matter components, one of which is a perfect fluid and the other two are interacting. The…
We investigate the cosmological evolution of an interacting phantom energy model in which the phantom field has interaction with the dark matter. We discuss the existence and stability of scaling solutions for two types of specific…
In this article, we investigate the existence of accelerating scaling solutions in coupled phantom cosmology without assuming any specific potential for the phantom scalar field. The coupling between phantom dark energy and dark matter is…
The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal…
The evolution of an homogeneous and isotropic dissipative fluid is analyzed using dynamical systems techniques. The dissipation is driven by bulk viscous pressure and the truncated Israel-Stewart theory is used. Although almost all…
Strongly correlated amorphous solids are a class of glass-formers whose inter-particle potential admits an approximate inverse power-law form in a relevant range of inter-particle distances. We study the steady-state plastic flow of such…
The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle…
We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations…