Related papers: Blowups and longtime developments with near-bounda…
We examine the idea that diffuse and giant molecular clouds and their substructure form as density fluctuations induced by large scale interstellar turbulence. We do this by investigating the topology of various fields in realistic…
We prove finite-time vorticity blowup for smooth solutions of the 2D compressible Euler equations with smooth, localized, and non-vacuous initial data. The vorticity blowup occurs at the time of the first singularity, and is accompanied by…
To date, most numerical simulations of molecular clouds, and star formation within them, assume a uniform density sphere or box with an imposed turbulent velocity field. In this work, we select molecular clouds from galactic scale…
The observed rapid onset of star formation in molecular clouds requires rapid formation of dense fragments which can collapse individually before being overtaken by global gravitationally-driven flows. Many previous investigations have…
In a previous work with Tai-Peng Tsai, the author studied the dynamics of axisymmetric, swirl-free Euler equation in four and higher dimensions. One conclusion of this analysis is that the dynamics become dramatically more singular as the…
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of…
New 13CO data from the BU-FCRAO Milky Way Galactic Ring Survey (GRS) are analyzed to understand the shape and internal motions of molecular clouds. For a sample of more than five hundred molecular clouds, we find that they are…
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime…
We summarize the current status of the turbulent model of star formation in turbulent molecular clouds. In this model, clouds, clumps and cores form a hierarchy of nested density fluctuations caused by the turbulence, and either collapse or…
A mixture of hard-sphere particles and model emulsion droplets is studied with a Brownian dynamics simulation. We find that the addition of nonwetting emulsion droplets to a suspension of pure hard spheres can lead to both gas-liquid and…
We demonstrate that the observationally inferred rapid onset of star formation after parental molecular clouds have assembled can be achieved by flow-driven cloud formation of atomic gas, using our previous three-dimensional numerical…
A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity equations for aggregation-diffusion macroscopic dynamics.…
We present semi-analytic dynamical models for giant molecular clouds evolving under the influence of HII regions launched by newborn star clusters. In contrast to previous work, we neither assume that clouds are in virial or energetic…
Molecular clouds are the principle stellar nurseries of our universe, keeping them in the focus of both observational and theoretical studies. From observations, some of the key properties of molecular clouds are well known but many…
Molecular clouds are supported by thermal pressure, magnetic pressure, and turbulent pressure. Each of these can be modeled with a polytropic equation of state, so that overall the total pressure is the sum of the individual components. We…
In this work, we study the behavior of blow-up solutions to the multidimensional restricted Euler--Poisson equations which are the localized version of the full Euler--Poisson system. We provide necessary conditions for the existence of…
The asymmetry in the cosmic microwave background (CMB) towards several nearby galaxies detected by Planck data is probably due to the rotation of "cold gas" clouds present in the galactic halos. In 1995 it had been proposed that galactic…
We prove a general, non-perturbative result about finite-time blowup solutions for the $L^2$-critical boson star equation $i\partial_t u = \sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under the sole assumption…
Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. It has been a long-standing open problem in astrophysics for…
In this paper we mainly investigate the initial value problem of the periodic Euler-Poincar\'e equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant…