Related papers: Local existence in retarded time under a weak deca…

Assuming initial data have small weighted $H^4\times H^3$ norm, we prove global existence of solutions to the Cauchy problem for systems of quasi-linear wave equations in three space dimensions satisfying the null condition of Klainerman.…

We show that, within a broad stationary-axisymmetric class, Kerr-type separability and hidden symmetry arise as a local consequence of the Einstein equations. Without assuming separability, algebraic speciality, Killing--Yano symmetry, or…

In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n+1$-dimensional, $n \geq 3$, spatially compact spacetimes which generalizes the $k=-1$…

We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in $R^3$. We introduce a new concept of dissipative weak solution of the problem based on a combination of the approach proposed by Judakov…

In this paper, we investigate the initial value problem for symmetric hyperbolic systems on globally hyperbolic Lorentzian manifolds with potentials that are both nonlocal in time and space. When the potential is retarded and uniformly…

We consider solutions of the Einstein vacuum equations which arise from smooth initial data on a hypersurface slightly inside a dynamical black hole settling down to a subextremal Kerr black hole, and satisfying a precise non-linear Price's…

Known entropy bounds, and the Generalized Second Law, were recently shown to imply bounds on the information arriving at future null infinity. We complete this derivation by including the contribution from gravitons. We test the bounds in…

We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends…

We study the initial value problem of the Einstein-Dirac system, and show the stability of the Minkowski solution in the massless case with the use of generalized wave coordinates. This requires the understanding of the Dirac equation in…

In this paper, we prove that the existence and uniqueness of globally weak solutions to the Cauchy problem for the weakly dissipative Camassa-Holm equation in time weighted $H^1$ space. First, we derive an equivalent semi-linear system by…

As a continuation of Part I [8], a more precise formulation of local time and local system is given. The observation process is reflected in order to give a relation between the classical physics for centers of mass of local systems and the…

The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in $H^1$ initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of…

We study decay properties for solutions to the initial value problem associated with the one-dimensional Zakharov-Rubenchik/Benney-Roskes system. We prove time-integrability in growing compact intervals of size $t^{r}$, $r<2/3$, centered on…

We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…

In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the…

To understand the formations of singularities of the Euler-Poisson system with vacuum, we revisit Makino's star model in this article. We first remedy, to some extent, the inconveniences of Makino's star model and remove its imposed…

In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity…

We discuss the Freund-Rubin compactification with cosmological constant and the dilaton field, and examine the stability of the spacetimes at the low energy. The Minkowski or de Sitter spacetime can be obtained if the dilation field is…

We prove that global hyperbolicity is stable in the interval topology on the spacetime metrics. We also prove that every globally hyperbolic spacetime admits a Cauchy hypersurface which remains Cauchy under small perturbations of the…

In this manuscript we consider an isotropic modification for the Landau equation with Coulomb potential in three space dimensions. Global in time existence of weak solutions for even initial data is shown by employing a time…