Related papers: Spherically Symmetric Solutions of Multi-dimension…
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are…
This paper deals with the spherically symmetric flow of compressible viscous and polytropic ideal fluid in unbounded domain exterior to a ball in $\mathbb{R}^n$ with $n\ge2$. We show that the global solutions are convergent as time goes to…
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…
We find exact and explicit solutions of the axisymmetric MHD equations of a self-gravitating polytropic gas. These solutions are able to describe a flat (uniform density) subsonic internal core, contracting homologously, of a collapsing…
We present the exact equations governing the dynamics of a spherically-symmetric inhomogeneous model with n decoupled and non-comoving perfect fluids. Thanks to the use of physically meaningful quantities we write the set of 3+2n equations…
A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$, is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
In this paper we explore the theory of the anisotropic porous medium equation in the slow diffusion range. After revising the basic theory, we prove the existence of self-similar fundamental solutions (SSFS) of the equation posed in the…
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation,…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We study the asymptotic dynamics of multi-bubble solutions to the focusing energy-critical wave equation in five dimensions. Assuming that the solution asymptotically decomposes into a finite superposition of spatially separated bubbles…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
We analyze an alternative theory of gravity characterized by metrics that are tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is supposed to hold. The simplest expression for the action of gravitational field is…
Galaxies exhibit a variety of non-axisymmetric structure (bars, spiral structure, lopsided structure, etc.). These suggest the following general problem: what are the possible stationary configurations of a two-dimensional self-gravitating…
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…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
We construct explicit measure-valued solutions to the one-dimensional pressureless gas dynamics system in a strip-like domain by introducing a new boundary potential. The constructed solutions satisfy an entropy condition, and depending on…
The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…
Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot…