相关论文: Well-posed geometric boundary data in General Rela…
In this paper, we consider the initial boundary value problem in a cylindrical domain to the three dimensional primitive equations with full eddy viscosity in the momentum equations but with only horizontal eddy diffusivity in the…
A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…
We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…
We consider a free boundary problem for the axially symmetric incompressible ideal magnetohydrodynamic equations that describes the motion of the plasma in vacuum. Both the plasma magnetic field and vacuum magnetic field are tangent along…
We study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl type equations that are derived from the incompressible MHD system with non-slip boundary condition on the velocity and…
Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions…
The present paper is devoted to the study of the well-posedness issue for the density-dependent Euler equations in the whole space. We establish local-in-time results for the Cauchy problem pertaining to data in the Besov spaces embedded in…
An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite…
A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy…
Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a…
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological…
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 present a new derivation of gravitational entropy functionals in higher-curvature theories of gravity using corner terms that are needed to ensure well-posedness of the variational principle in the presence of corners. This is…
In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…
The initial boundary-value problem (IBVP) and the Cauchy problem for the Kuramoto--Sivashinsky equation and other related $2m$th-order semilinear parabolic partial differential equations in one and N dimensions are considered. Global…