相关论文: Decoupled energy estimates for tensorial non-linea…
We use an important decoupling property of gravitational field equations in the general relativity theory and modifications, written with respect to nonholonomic frames with 2+2 spacetime decomposition. This allows us to integrate the…
The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his pseudotensor. It is now understood that energy-momentum is \emph{quasi-local} (associated with a closed 2-surface). Here we consider…
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify…
We investigate a semilinear wave equation with energy-critical nonlinearity and a nonlinear damping mechanism driven by the total energy of the system. The model combines the quintic defocusing term with a time-dependent dissipation of the…
In this article, we make use of a weight function capturing the concentration phenomenon of unstable future-trapped causal geodesics. A projection $V_+$, on the tangent space of the null-shell, of the associated symplectic gradient turns…
In this paper we study the behaviors of the the energy of solutions of coupled wave equations on a compact manifold with boundary in the case of indirect nonlinear damping . Only one of the two equations is directly damped by a localized…
In this work a system of non-linear elliptic equations is considered, where the non-linear term is the sum of a quadratic form and a Sobolev sub-critical term. An extra assumption is introduced on the sub-critical term, which is minimal…
We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a…
A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical…
We study solutions to the Yang-Mills-Higgs equations on the maximal Cauchy development of the data given on a ball of radius $R$ in $\mathbb{R}^3$. The energy of the data could be infinite and the solution grows at most inverse polynomially…
We investigate a linearized tensor-tensor theory of gravity with torsion and a perturbed torsion wave solution is discovered in background Minkowski spacetime with zero torsion. Furthermore, gauge transformations of any perturbed tensor…
We give a new decay framework for general dissipative hyperbolic system and hyperbolic-parabolic composite system, which allow us to pay less attention on the traditional spectral analysis in comparison with previous efforts. New…
In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is taken to be an arbitrary smooth function without…
It is known that there exist solutions with interfaces to various scalar nonlinear wave equations. In this paper, we look for solutions of a two-component system of nonlinear wave equations where one of the components has an interface and…
Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles, whose average value agrees with expressions derived previously. We analyze the relation…
To build a self-consistent effective-one-body (EOB) theory, in which the Hamiltonian, radiation-reaction force and waveform for the "plus" and "cross" modes of the gravitational wave should be based on the same effective background…
We prove global existence for solutions arising from small initial data for a large class of quasilinear wave equations satisfying the `weak null condition' of Lindblad and Rodnianski, significantly enlarging upon the class of equations for…
We continue the study of the Dirichlet boundary value problem of nonlinear wave equation with radial data in the exterior $\Omega = \mathbb{R}^3\backslash \bar{B}(0,1)$. We combine the distorted Fourier truncation method in…
The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives,…
One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric into a background metric plus perturbation.…