Zobrazeno 1 - 10
of 231
pro vyhledávání: '"Rodnianski, Igor"'
We prove global existence, boundedness and decay for small data solutions $\psi$ to a general class of quasilinear wave equations on Kerr black hole backgrounds in the full sub-extremal range $|a|
Externí odkaz:
http://arxiv.org/abs/2410.03639
Autor:
Ginsberg, Daniel, Rodnianski, Igor
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our analysis is mo
Externí odkaz:
http://arxiv.org/abs/2403.13568
Autor:
Bringmann, Bjoern, Rodnianski, Igor
We first introduce a new model for a two-dimensional gauge-covariant wave equation with space-time white noise. In our main theorem, we obtain the probabilistic global well-posedness of this model in the Lorenz gauge. Furthermore, we prove the failur
Externí odkaz:
http://arxiv.org/abs/2302.14271
We prove global existence and decay for small-data solutions to a class of quasilinear wave equations on a wide variety of asymptotically flat spacetime backgrounds, allowing in particular for the presence of horizons, ergoregions and trapped null ge
Externí odkaz:
http://arxiv.org/abs/2212.14093
Autor:
Czimek, Stefan, Rodnianski, Igor
In this paper we develop a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to the previous constru
Externí odkaz:
http://arxiv.org/abs/2210.09663
This is the third paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We provide full details of our characteristic gluing (including the $10$ charges) of strongly asymptotically flat data to the
Externí odkaz:
http://arxiv.org/abs/2107.02456
This is the second paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-$10$ characteristic gluing problem for characteristic data which are close to the Minkowski data. W
Externí odkaz:
http://arxiv.org/abs/2107.02449
In this paper we introduce the characteristic gluing problem for the Einstein vacuum equations. We present a codimension-$10$ gluing construction for characteristic initial data which are close to the Minkowski data and we show that the $10$-dimensio
Externí odkaz:
http://arxiv.org/abs/2107.02441
We prove the non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region: general vacuum initial data, with no symmetry assumed, sufficiently close to Schwarzschil
Externí odkaz:
http://arxiv.org/abs/2104.08222
Publikováno v:
Journal of the American Mathematical Society, volume 36, number 3, 2023
For $(t,x) \in (0,\infty)\times\mathbb{T}^D$, the generalized Kasner solutions are a family of explicit solutions to various Einstein-matter systems that start out smooth but then develop a Big Bang singularity as $t \downarrow 0$, i.e., curvature bl
Externí odkaz:
http://arxiv.org/abs/2012.05888