Related papers: On the Initial Data Constraints on the Light cone …
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
In this paper, we establish a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, the $\gamma$-gas law equation of state for $\gamma=2$ and the general initial density $\ri \in H^5$.…
There has been recent progress in developing well-posed theories of relativistic viscous hydrodynamics and of gravitational effective field theories. These have in common the feature that they introduce unphysical degrees of freedom. We…
In the present paper, some aspects of the finite-dimensional theory of set-inclusive generalized equations are studied. Set-inclusive generalized equations are problems arising in several contexts of optimization and variational analysis,…
The modified Gauss-Bonnet gravity can be motivated by a number of physical reasons, including: the uniqueness of a gravitational Lagrangian in four and higher dimensions and the leading order $\alpha^\prime$ corrections in superstring…
If there is a null gradient field in 1+3 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is much helpful for simplifying and…
Initial-boundary value problems in a strip with different types of boundary conditions for two-dimensional generalized Zakharov--Kuznetsov equation are considered. Results on global existence and uniqueness of weak solutions in certain…
The nature of dark matter and dark energy are among the central questions in cosmology. Strong gravitational lenses with multiple source planes provide a geometric probe of cosmology: the ratio of deflection angles at different redshifts…
We show the stability of the geometric optics approximation in general relativity by constructing a family $(g_\lambda)_{\lambda\in(0,1]}$ of high-frequency metrics solutions to the Einstein vacuum equations in 3+1 dimensions without any…
We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under…
The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
We study a constrained minimum energy problem with an external field relative to the Riesz kernel of an arbitrary order for a generalized condenser with touching oppositely-charged plates. Conditions sufficient for the solvability of the…
We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this paper, we…
Einstein's general relativity relates the curvature of space time, a second order differential property, to the stress-energy-momentum tensor. In this paper we ask whether it is possible to develop a first order theory relating space-time…
A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the…