Related papers: Global Dynamics, Blow-Up, and Bianchi Cosmology
We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat…
In this paper, we analyze the dynamics of an $N$ particles system evolving according the gradient flow of an energy functional. The particle system is a consistent approximation of the Lagrangian formulation of a one parameter family of…
It is commonly stated that we have entered the era of precision cosmology in which a number of important observations have reached a degree of precision, and a level of agreement with theory, that is comparable with many Earth-based physics…
Pressureless Euler-Poisson equations with attractive forces are standard models in Newtonian cosmology. In this article, we further develop the spectral dynamics method and apply a novel spectral-dynamics-integration method to study the…
We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we…
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…
We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
Bianchi type V string cosmological models in general relativity are investigated. To get the exact solution of Einstein's field equations, we have taken some scale transformations followed by Camci $\it et ~ al$ (2001). It is shown that…
In this work we study a system of Schr\"odinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in…
We study existence, uniqueness, multiplicity and symmetry of large solutions for a class of quasi-linear elliptic equations. Furthermore, we characterize the boundary blow-up rate of solutions, including the case where the contribution of…
Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…
An unresolved question in inflationary cosmology is the assignment of probabilities to different types of events that can occur in the eternally inflating multiverse. We explore the possibility that the resolution of this "measure problem"…
We point out a new phenomenon which seems to be generic in 4d effective theories of scalar fields coupled to Einstein gravity, when applied to cosmology. A lift of such theories to a Weyl-invariant extension allows one to define classical…
We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some…
Multidimensional cosmological model describing the evolution of a fluid with shear and bulk viscosity in $n$ Ricci-flat spaces is investigated. The barotropic equation of state for the density and the pressure in each space is assumed. The…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical…