Related papers: Blowups and longtime developments with near-bounda…
It is well-known that the two-dimensional Keller-Segel system admits finite time blowup solutions, which is the case if the initial density has a total mass greater than $8\pi$ and a finite second moment. Several constructive examples of…
We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of…
The existence of substellar cold H2 globules in planetary nebulae and the mere existence of comets suggest that the physics of cold interstellar gas might be much richer than usually envisioned. We study the case of a cold gaseous medium in…
We study numerically the formation of molecular clouds in large-scale colliding flows including self-gravity. The models emphasize the competition between the effects of gravity on global and local scales in an isolated cloud. Global…
The star-forming ability of a molecular cloud depends on the fraction of gas it can cycle into the dense-phase. Consequently, one of the crucial questions in reconciling star-formation in clouds is to understand the factors that control…
The observational record of turbulence within the molecular gas phase of the interstellar medium is summarized. We briefly review the analysis methods used to recover the velocity structure function from spectroscopic imaging and the…
Gravitational-collapse-based explanations of the cosmic web lead to problems in estimating the total mass in the universe. A first-principles several-scales model is developed here for the structural organisation of cosmic matter in a flat…
In this paper we present a method for extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimension,…
In this paper, the finite time blow-up of smooth solutions to the Cauchy problem for full Euler-Poisson equations and isentropic Euler-Poisson equations with repulsive forces or attractive forces in high dimensions $(n\geq3)$ is proved for…
We present a comprehensive study of MHD waves and instabilities in a weakly ionised system, e.g., an interstellar molecular cloud. We determine all the critical wavelengths of perturbations across which the sustainable wave modes can change…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…
We review the properties of turbulent molecular clouds (MCs), focusing on the physical processes that influence star formation (SF). MC formation appears to occur during large-scale compression of the diffuse ISM driven by supernovae,…
In this paper we consider smooth solutions of the Navier--Stokes equations with a linear dependence on the spatial variable. We reduce the evolution of these solutions to a matrix ODE, and show that there are such solutions that blowup in…
We derive the mass function of condensations (clumps) which were formed through a turbulent cascade over a range of spatial scales $L\le20$ pc during early, predominantly turbulent evolution of a molecular cloud. The approach rests upon the…
We revisit the origin of Larson's scaling relations, which describe the structure and kinematics of molecular clouds, based on recent observations and large-scale simulations of supersonic turbulence. Using dimensional analysis, we first…
We explore the constraints on globular cluster formation provided by the observed conditions in starbursts where globulars are currently forming, and by the observed properties of young and old globular clusters. We note that the pressure…
We construct spacetimes which provide spherical and nonspherical models of black hole formation in the flat Friedmann--Lemaitre--Robertson--Walker (FLRW) universe with the Lemaitre--Tolman--Bondi solution and the Szekeres quasispherical…
We study some examples of collective behavior in neutrino clouds governed by the neutral-current neutrino-neutrino interaction. The standard equations for analyzing such systems are rederived in a two-step process: first, a replacement of…
We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic blow-up point at the origin, and a blow-up surface which is…
We provide a scenario for a singularity-mediated turbulence based on the self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth initial states leads to blow-up in finite time. Here, by adding dissipation, these…