Related papers: Blowups and longtime developments with near-bounda…
We discuss the lifetimes and evolution of clumps and cores formed as turbulent density fluctuations in nearly isothermal molecular clouds. In the non-magnetic case, clumps are unlikely to reach a hydrostatic state, and instead are expected…
The Newtonian Euler-Poisson equations with attractive forces are the classical models for the evolution of gaseous stars and galaxies in astrophysics. In this paper, we use the integration method to study the blowup problem of the…
Shocks in granular media, such as vertically oscillated beds, have been shown to develop instabilities. Similar jet formation has been observed in explosively dispersed granular media. Our previous work addressed this instability by…
We study the formation of singularity for the isothermal Euler-Poisson system arising from plasma physics. Contrast to the previous studies yielding only limited information on the blow-up solutions, for instance, sufficient conditions for…
We propose and investigate a new formation mechanism for globular clusters in which they form within molecular clouds that are formed in the shocked regions created by galactic winds driven by successive supernova explosions shortly after…
Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin…
We consider a model of cell motion with boundary signal production which describes some aspects of eukaryotic cell migration. Generic polarity markers located in the cell are transported by actin which they help to polymerize. This leads to…
The recent paper by Heyer et al (2009) indicates that observations of size, linewidth and column density of interstellar clouds do not agree with simple virial equilibrium (VE) as a balance between gravitational and kinetic energies in the…
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of…
The diffusion-driven growth of a dense cloud of bubbles immersed in a gas-supersaturated liquid is a problem that finds applications in several modern technologies such as solvent-exchange micro-reactors, nanotechnology or the manufacturing…
This paper concerns the finite-time blow-up and asymptotic behaviour of solutions to nonlinear Volterra integrodifferential equations. Our main contribution is to determine sharp estimates on the growth rates of both explosive and…
A class of semi-bounded solutions of the two-dimensional incompressible Euler equations satisfying either periodic or Dirichlet boundary conditions is examined. For smooth initial data, new blowup criteria in terms of the initial concavity…
During the last two decades, the focus of star formation research has shifted from understanding the collapse of a single dense core into a star to studying the formation hundreds to thousands of stars in molecular clouds. In this chapter,…
We present a detailed analysis comparing the velocity fields in molecular clouds and the atomic gas that surrounds them in order to address the origin of the gradients. To that end, we present first-moment intensity-weighted velocity maps…
To understand the formation of a magnetically dominated molecular cloud out of an atomic cloud, we follow the dynamical evolution of the cloud with a time-dependent axisymmetric magnetohydrodynamic code. A thermally stable warm atomic cloud…
We recently proposed that the star-forming potential of dense molecular clouds in the Central Molecular Zone (CMZ, i.e. the central few 100 pc) of the Milky Way is linked to their orbital dynamics, potentially giving rise to an…
The dense molecular cloud cores that form stars, like other self-gravitating objects, undergo bulk oscillations. Just at the point of gravitational instability, their fundamental oscillation mode has zero frequency. We study, using…
Since Kolmogorov proposed his phenomenological theory of hydrodynamic turbulence in 1941, the description of mechanism leading to the energy cascade and anomalous scaling remains an open problem in fluid mechanics. Soon after, in 1949…
We present the results of a series of numerical simulations of compressible, self-gravitating hydrodynamic turbulence of cluster-forming clumps in molecular clouds. We examine the role that turbulence has in the formation of gravitationally…
We are concerned with the multi-bubble blow-up solutions to rough nonlinear Schr\"odinger equations in the focusing mass-critical case. In both dimensions one and two, we construct the finite time multi-bubble solutions, which concentrate…