Related papers: Blowups and longtime developments with near-bounda…
In this work, we present a new type of scalar clouds supported by spherically symmetric horizonless compact objects in the scalar-Gauss-Bonnet theory. Unlike the previous spontaneous scalarization that is triggered by the tachyonic…
{It has recently been proposed that giant molecular complexes form at the sites where streams of diffuse warm atomic gas collide at transonic velocities.} {We study the global statistics of molecular clouds formed by large scale colliding…
Massive stars influence their parental molecular cloud, and it has long been suspected that the development of hydrodynamical instabilities can compress or fragment the cloud. Identifying such instabilities has proved difficult. It has been…
Nobel Prize laureate P.J.E. Peebles [24] has emphasized the importance and difficulties of studying the large scale clustering of matter in cosmology. Nonlinear gravitational instability plays a central role in understanding the clustering…
In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - \Delta u = u^{p}$ in three space dimensions. We show that for generic large initial…
Molecular Cloud Complexes (MCCs) are highly structured and ``turbulent''. Observational evidence suggests that MCCs are dynamically dominated systems, rather than quasi-equilibrium entities. The observed structure is more likely a…
In this paper, we study the blowup phenomena for the regular solutions of the isentropic relativistic Euler-Poisson equations with a vacuum state in spherical symmetry. Using a general family of testing functions, we obtain new blowup…
Observational evidence from local star-forming regions mandates that star formation occurs shortly after, or even during, molecular cloud formation. Models of the formation of molecular clouds in large-scale converging flows have identified…
The classical picture of a star-forming filament is a near-equilibrium structure, with collapse dependent on its gravitational criticality. Recent observations have complicated this picture, revealing filaments as a mess of apparently…
It appears that the majority of rapidly-, well-localized gamma-ray bursts with undetected, or dark, optical afterglows, or `dark bursts' for short, occur in clouds of size R > 10L_{49}^{1/2} pc and mass M > 3x10^5L_{49} M_{sun}, where L is…
For the prescribed scalar curvature equation on $S^n$ ($n \ge 6$), we consider the situation where the number of bubbles tends to infinity in the Lyapunov-Schmidt (finite dimension) reduction method. In an outstanding paper by Wei and Yan,…
We review the progress made in understanding molecular cloud formation and evolution toward star formation since the first Crete conference in 1990. It now seems clear that molecular clouds in the Galaxy at least form from compressed HI…
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…
We employ granular hydrodynamics to investigate a paradigmatic problem of clustering of particles in a freely cooling dilute granular gas. We consider large-scale hydrodynamic motions where the viscosity and heat conduction can be…
The cloud-scale physics of star formation and feedback represent the main uncertainty in galaxy formation studies. Progress is hampered by the limited empirical constraints outside the restricted environment of the Local Group. In…
The primitive equations (PEs) model large scale dynamics of the oceans and the atmosphere. While it is by now well-known that the three-dimensional viscous PEs is globally well-posed in Sobolev spaces, and that there are solutions to the…
Two-fold singularities in a piecewise smooth (PWS) dynamical system in $\mathbb{R}^3$ have long been the subject of intensive investigation. The interest stems from the fact that trajectories which enter the two-fold are associated with…
This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…
We study the formation of singularity for the Euler-Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic…
We construct a large class of spacetimes that are smoothly matched to homogeneous, spherically symmetric clouds of matter. The evolution of the clouds is left arbitrary to allow for the incorporation of modifications by quantum effects,…