Related papers: Characteristic Initial Value Problem for Spherical…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…
We consider the equations of a multi-velocity model of a binary mixture of viscous compressible fluids (two-fluid medium) in the case of one-dimensional barotropic motions. We prove the global (in time) existence and uniqueness of a strong…
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a…
We study an initial boundary value problem on a ball for the heat-conductive system of compressible Navier-Stokes-Fourier equations, in particular, a criterion of breakdown of the classical solution. For smooth initial data away from…
We consider the equations which describe polytropic one-dimensional flows of viscous compressible multifluids. We prove global existence and uniqueness of a solution to the initial-boundary value problem which corresponds to the flow in a…
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding…
In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we…
We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…
A class of exact spherically symmetric perturbations of retarding automodel solutions linearized around Friedman background of Einstein equations for an ideal fluid with an arbitrary barotrope value is obtained and investigated.
We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…
The initial-boundary value problem of the vorticity equation has been solved numerically by an iterative method. A variety of initial vorticity distributions is specified. All of them can be described by simple mathematical functions: there…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
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…
The paper concerns the problem for the ultrahyperbolic equation in the Euclidean space with data on a characteristic hyperplane. Smoothness and asymptotics of the solution along characteristic lines transversal to the initial hyperplane are…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
By applying the theory of group-invariant solutions we investigate the symmetries of Ricci flow and hyperbolic geometric flow both on Riemann surfaces. The warped products on $\mathcal {S}^{n+1}$ of both flows are also studied.
In this paper, we are exploring some of the properties of the self-similar solutions of the first kind. In particular, we shall discuss the kinematic properties and also check the singularities of these solutions. We discuss these…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
We investigate the interaction of two oncoming shock waves in spherical symmetry for an ideal barotropic fluid. Our research problem is how to establish a local in time solution after the interaction point and determine the state behind the…