相关论文: Hyperbolicity of Hamiltonian formulations in Gener…

We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our…

The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free…

Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological…

The Hamiltonian dynamics of a compressible inviscid fluid is formulated as a gauge theory. The idea of gauge equivalence is exploited to unify the study of apparantly distinct physical problems and solutions of new models can be generated…

The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…

Assuming as starting point the validity of the Einstein-Rosen metric, we study the hyperbolic system of P.D.E. to which the Einstein's field's equations can be reduced. We prove using the implicit function theorem in Banach spaces, the…

In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann…

We show in this article how the usual hamiltonian formalism of General Relativity should be modified in order to allow the inclusion of the Euclidean classical solutions of Einstein's equations. We study the effect that the dynamical change…

We consider the most general class of teleparallel theories of gravity quadratic in the torsion tensor, and carry out a detailed investigation of its Hamiltonian formulation in the time gauge. Such general class is given by a…

A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by…

The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…

The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the…

There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. The resolution, a Hamiltonian system on a unified symplectic…

We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…

The Hamiltonian formulation of Mimetic Gravity is formulated. Although there are two more equations than those of general relativity, these are proved to be the constraint equation and the conservation of energy-momentum tensor. The Poisson…

Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…

We consider symmetries and perturbed symmetries of canonical Hamiltonian equations of motion. Specifically we consider the case in which the Hamiltonian equations exhibit a Lambda symmetry under some Lie point vector field. After a brief…

The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian…

Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.

A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…