Related papers: Spherical Isothermal Self-Similar Shock Flows
This work presents a comprehensive study of the microlocal energy decomposition and propagation of singularities for semiclassically adjusted dissipative pseudodifferential operators. The analysis focuses on the behavior of energy…
Coughlin et al. (2018) (Paper I) derived and analyzed a new regime of self-similarity that describes weak shocks (Mach number of order unity) in the gravitational field of a point mass. These solutions are relevant to low energy explosions,…
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation…
We describe similarity solutions that characterize the collapse of collisional gas onto scalefree perturbations in an Einstein-de Sitter universe. We consider the effects of radiative cooling and derive self-similar solutions under the…
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS). CSS is $L^{2}$-critical, admits solitons, and has the pseudoconformal symmetry. In this work, we consider pseudoconformal blow-up solutions under $m$-equivariance,…
We obtain self-similar solutions that describe the dynamics of a self-gravitating, rotating, viscous system. We use simplifying assumptions; but explicitly include viscosity and the cooling due to the dissipation of energy. By assuming that…
We prove that Guderley's self-similar imploding shock solution for the compressible Euler equations with ideal--gas law ($\gamma>1$) arises from classical, radially symmetric, shock--free data. For such data prescribed at initial time…
We investigate self-similar magnetohydrodynamic (MHD) processes in an isothermal self-gravitating fluid with a quasi-spherical symmetry and extend the envelope expansion with core collapse (EECC) solutions of Lou & Shen by incorporating a…
Shocks due to hyperbolic partial differential equations (PDEs) appear throughout mathematics and science. The canonical example is shock formation in the inviscid Burgers' equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial…
The general problem of shock formation in three space dimensions was solved by D. Christodoulou in his 2007 monograph: 'The Formation of Shocks in 3-dimensional Fluids'. In this work also a complete description of the maximal development of…
We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are…
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispersive} solution when singularities give rise to a graph of…
We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an adaptive grid. We show that this…
In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or…
A self-similar formalism for the study of the gravitational collapse of molecular gas provides an important theoretical framework from which to explore the dynamics of star formation. Motivated by the presence of elongated and filamentary…
We present a mathematical model for the propagation of the shock waves that occur during planetary collisions. Such collisions are thought to occur during the formation of terrestrial planets, and they have the potential to erode the…
An explosively generated shockwave with time-dependent radius $R(t)$ is characterized by a phase in which the shocked gas becomes radiative with an effective adiabatic index $\gamma \simeq 1$. Using the result that the post-shock gas is…
We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=\alpha\mu$. We identify for the first time the global…
We construct conformastat spherically symmetric spacetimes representing anisotropic fluid matter distributions from given solutions of the Poisson's equation of Newtonian gravity and its corresponding circular speed profile. As simple…
For $0<\alpha<\frac{1}{3}$ we construct unique solutions to the fractal Burgers equation $\partial_t u + u\partial_xu + (-\Delta)^\alpha u = 0$ which develop a first shock in finite time, starting from smooth generic initial data. This…