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Recent models of molecular cloud formation and evolution suggest that such clouds are dynamic and generally exhibit gravitational collapse. We present a simple analytic model of global collapse onto a filament and compare this with our…
We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances…
The molecular component of the Galaxy is comprised of turbulent, magnetized clouds, many of which are self-gravitating and form stars. To understand how these clouds' evolution may depend on their level of turbulence, mean magnetization,…
The universality of interstellar turbulence is examined from observed structure functions of 27 giant molecular clouds and Monte Carlo modeling. We show that the structure functions, dv=v0 l^gamma, derived from wide field imaging of CO…
We present numerical simulations of the passage of clumpy gas through a galactic spiral shock and the subsequent formation of giant molecular clouds (GMCs). The spiral shock forms dense clouds while dissipating kinetic energy, producing…
The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account,…
The fragmentation of gas to form stars in molecular clouds is intrinsically linked to the turbulence within them. These internal motions are set at the birth of the cloud and may vary with galactic environment and as the cloud evolves. In…
We investigate the chemical evolution of a forming molecular cloud behind an interstellar shock wave. We conduct three-dimensional magnetohydrodynamics simulations of the converging flow of atomic gas, including a simple chemical network…
Dense cores inherit turbulent motions from the interstellar medium in which they form. As a tool for comparison to both simulations and observations, it is valuable to construct theoretical core models that can relate their internal density…
The mass and size distributions are the key characteristics of any astrophysical objects, including the densest clumps comprising the cold phase of multiphase environments. In our recent papers, we showed how individual clouds of various…
The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a…
We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we…
The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with swirl. The simulations…
We propose a simple analytic theory for environmentally-dependent molecular cloud lifetimes, based on the large-scale (galactic) dynamics of the interstellar medium. Within this theory, the cloud lifetime is set by the time-scales for…
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast…
Complex turbulent motions are ubiquitously observed in many astrophysical systems. Their origin, however, is still poorly understood. When cosmic structures form, they grow in mass via accretion from the surrounding environment. We propose…
To investigate how molecular clouds react to different environmental conditions at a galactic scale, we present a catalogue of giant molecular clouds resolved down to masses of $\sim 10$~M$_{\odot}$ from a simulation of the entire disc of…
This paper contributes to the study of large data problems for $C^1$ solutions of the relativistic Euler equations. In the $(1+1)$-dimensional spacetime setting, if the initial data are away from vacuum, a key difficulty in proving the…
Motivated by the analysis of the propagation of internal waves in a stratified ocean, we consider in this article the incompressible Euler equations with variable density in a flat strip, and we study the evolution of perturbations of the…
We propose that inward, subsonic flows arise from the local dissipation of turbulent motions in molecular clouds. Such "turbulent cooling flows" may account for recent observations of spatially extended inward motions towards dense cores.…