相关论文: Global existence problem in $T^3$-Gowdy symmetric …

We prove existence and boundedness of classical solutions for a family of viscous conservation laws in one space dimension for arbitrarily large time. The result relies on H. Amann's criterion for global existence of solutions and on…

This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, asymptotically flat, and notably, non-stationary spacetimes.…

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such…

We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and…

We investigate the canonical quantization of supergravity N=1 in the case of a midisuperspace described by Gowdy $T^3$ cosmological models. The quantum constraints are analyzed and the wave function of the universe is derived explicitly.…

In this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named the Jordan--Moore--Gibson--Thompson equation. This equation arises as an alternative model to the well-known Kuznetsov equation in acoustics. We prove…

Global cosmic strings are generically predicted in particle physics beyond the Standard Model, e.g., a post-inflationary global $U(1)$ symmetry breaking which may associate with axion-like dark matter. We demonstrate that although…

This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…

The complete set of solutions of two dimensional classical string theory are constructed for any curved spacetime. They describe folded strings moving in curved spacetime. Surprizing stringy behavior becomes evident at singularities such as…

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…

In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding…

We address the global-in-time existence and pathwise uniqueness of solutions for the stochastic incompressible Navier-Stokes equations with a multiplicative noise on the three-dimensional torus. Under natural smallness conditions on the…

We consider the gravity water waves system in the case of a one dimensional interface, for sufficiently smooth and localized initial data, and prove global existence of small solutions. This improves the almost global existence result of Wu…

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…

In this paper, we present a partial result on the global well-posedness of the Cauchy problem for the Einstein-Yang-Mills system in the constant mean extrinsic curvature spatial harmonic and generalized Coulomb gauges as introduced in…

Some of the most interesting results on the global dynamics of solutions of the vacuum Einstein equations concern the Gowdy spacetimes whose spatial topology is that of a three-dimensional torus. In this paper certain of these ideas are…

This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…

We are presenting the basic ingredients of a stringy mechanism able to resolve both the Hagedorn instabilities of finite temperature superstrings as well as the initial singularity of the induced cosmology in arbitrary dimensions. These are…

We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of data allowing growth at spatial infinity. Namely, we show the global existence of suitable weak solutions when the initial data…

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…