Related papers: Blowups and longtime developments with near-bounda…
Molecular gas disks are generally Toomre stable ($Q_T>$1) and yet clearly gravitationally unstable to structure formation as evidenced by the existence of molecular clouds and ongoing star formation. This paper adopts a 3D perspective to…
Molecular cloud observations show that clouds have non-thermal velocity dispersions that scale with the cloud size as $\sigma\propto R^{1/2}$ at constant surface density, and for varying surface density scale with both the cloud`s size and…
We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pressure gradients of the flow are considered to be negligible and so, the flow is ballistic.…
We investigate in this article the long-time behaviour of the solutions to the energy-dependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under…
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger…
The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth…
Recent progress in the understanding of star formation is summarized. A consistent picture is emerging where molecular clouds form with turbulent velocity fields and clumpy substructure, imprinted already during their formation. The clouds…
It is well-known that shock will form in finite time for hyperbolic conservation laws from initial nonlinear compression no matter how small and smooth the data are. Classical results, including Lax [14], Liu [22], Li-Zhou-Kong [16],…
Molecular clouds often exhibit filamentary or sheet-like shapes. We compute the free-fall time ($\tff$) for finite, uniform, self-gravitating circular sheets and filamentary clouds of small but finite thickness, so that their volume density…
We simulate fragmentation and gravitational collapse of cold, magnetized molecular clouds. We explore the nonlinear development of an instability mediated by ambipolar diffusion, in which the collapse rate is intermediate to fast…
The formation of astrophysical structures, such as stars, compact objects but also galaxies, entail an,enhancement of densities by many orders of magnitude which occurs through gravitational collapse. The role played by turbulence during…
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping…
We suggest that molecular clouds can be formed on short time scales by compressions from large scale streams in the interstellar medium (ISM). In particular, we argue that the Taurus-Auriga complex, with filaments of 10-20 pc $\times$ 2-5…
We used CO (2-1) and CO (1-0) data cubes to identify molecular clouds and study their kinematics and dynamics in three nearby galaxies and the inner Milky Way. When observed at similar spatial and velocity resolutions, molecular clouds in…
In this paper we study the finite time blow-up problem for the axisymmetric 3D incompressible Euler equations with swirl. The evolution equations for the deformation tensor and the vorticity are reduced considerably in this case. Under the…
We study existence of global solutions and finite time blow-up of solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term $\rho(x) u^p$ with $p>1$; this is a…
This paper is devoted to the blow-up of analytic solutions with the emergence of irregular solutions.
We present the exact solutions for the collapse of a spherically-symmetric, cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These…
Using the adaptive mesh refinement code MG, we perform hydrodynamic simulations of the interaction of a shock with a molecular cloud evolving due to thermal instability and gravity. To explore the relative importance of these processes,…
It is known that smooth solutions to the non-isentropic Navier-Stokes equations without heat-conductivity may lose their regularities in finite time in the presence of vacuum. However, in spite of the recent progress on such blowup…