Related papers: Hawking Mass Monotonicity for Initial Data Sets
In three spatial dimensions, we study the Cauchy problem for the model wave equation $- \partial_t^2 \Psi + (1 + \Psi)^P \Delta \Psi = 0$ for $P \in \lbrace 1,2 \rbrace$. We exhibit a stable form of finite-time Tricomi-type degeneracy…
This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial…
In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. Based on estimates developed in [Buckmaster-De Lellis-Isett-Sz\'ekelyhidi], we prove that the set of H\"older $1\slash 5-\eps$ wild…
We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…
We propose a logarithmic parametrization form of energy density for the scalar field dark energy in the framework of the standard theory of gravity, which supports the necessary transition from the decelerated to the accelerated behavior of…
In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump conditions on the metric and second fundamental…
Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
We prove well-posedness of the initial value problem for the Einstein equations for spatially-homogeneous cosmologies with data at an isotropic cosmological singularity, for which the matter content is either a cosmological constant with…
We study the formation of singularities for the curvature flow of networks when the initial data is symmetric with respect to a pair of perpendicular axes and has two triple junctions. We show that, in this case, the set of singular times…
We rigorously establish the existence of dark-bright solitons as traveling wave solutions to a one dimensional defocusing Gross-Pitaevskii system, a widely used model for describing mixtures of Bose-Einstein condensates and nonlinear…
By considering families of radial null geodesics, we study the subsets of initial data that lead to naked singularities and black holes in inhomogeneous spherical dust collapse. We introduce the notion of central homogeneity for spherical…
We generalize the analytical expressions for the two-loop leading-log neutral Higgs boson masses and mixing angles to the case of general left- and right-handed soft supersymmetry breaking stop and sbottom masses and left--right mixing mass…
We give a family of monotone quantities along smooth solutions to the inverse curvature flows in Euclidean spaces. We also derive a related geometric inequality for closed hypersurfaces with positive k-th mean curvature.
In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in…
We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
We study the masses of the Higgs bosons in the most general two-Higgs-doublet model in a basis-independent approach. We adapt the recently developed Minkowski-space formalism to this problem and calculate traces of any power of the…
The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption…
The thermodynamic properties of dark energy-dominated universe in the presence of a black hole are investigated in the general case of a varying equation-of-state-parameter $w(a)$. We show that all the thermodynamics quantities are regular…