Related papers: Spherical Isothermal Self-Similar Shock Flows
We present a new class of solutions to Einstein equations for the spherical collapse of dustlike matter coupled with heat flux. In this family of solutions spacetime shear is necessarily non-zero. Also these solutions have an interesting…
Stars and planets move supersonically in a gaseous medium during planetary engulfment, stellar interactions and within protoplanetary disks. For a nearly uniform medium, the relevant parameters are the Mach number and the size of the body,…
Guderley's 1942 work on radial shock waves provides cases of self-similar Euler flows exhibiting blowup of primary (undifferentiated) flow variables: a converging shock wave invades a quiescent region, and the velocity and pressure in its…
Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows the…
We are concerned with geometric properties of transonic shocks as free boundaries in two-dimensional self-similar coordinates for compressible fluid flows, which are not only important for the understanding of geometric structure and…
A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. This formalism also…
This paper addresses the construction and the stability of self-similar solutions to the isentropic compressible Euler equations. These solutions model a gas that implodes isotropically, ending in a singularity formation in finite time. The…
We present a new method for analyzing the global stability of the Sedov-von Neumann-Taylor self-similar solutions, describing the asymptotic behavior of spherical decelerating shock waves, expanding into ideal gas with density \propto…
We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are…
Understanding the flow behaviors of supercooled liquids presents a major challenge in liquid-state physics due to the strong nonlinearity and rich phenomena. To unravel this complexity, we introduce the concept of local configurational…
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…
The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative…
We study the propagation of a Newtonian shock in a spherically symmetric, homologously expanding ejecta. We focus on media with a steep power-law density profile of the form $\rho \propto t^{-3}v^{-\alpha}$, with $\alpha>5$, where $v$ is…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
In this work we consider the problem of constructing initial conditions for a flow model such that the resulting flow evolution leads to a self-similar energy cascade consistent with Kolmogorov's statistical theory of turbulence. As a first…
The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of…
Well-resolved galaxy clusters often show a large-scale quasi-spiral structure in deprojected density $\rho$ and temperature $T$ fields, delineated by a tangential discontinuity known as a cold front, superimposed on a universal radial…
This paper concerns the construction and analysis of a new family of exact general relativistic shock waves. The construction resolves the open problem of determining the expanding waves created behind a shock-wave explosion into a static…
We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically simmetric space--time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…