Zobrazeno 1 - 10
of 128
pro vyhledávání: '"Rodnianski, I"'
Autor:
Klainerman, S., Rodnianski, I.
This is a follow up on our previous work in which we have presented a modified, simpler version of the remarkable recent result of Christodoulou on the formation of trapped surfaces. In this paper we prove two related results. First we extend the sem
Externí odkaz:
http://arxiv.org/abs/1002.2656
Autor:
Klainerman, S., Rodnianski, I.
In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial conditions
Externí odkaz:
http://arxiv.org/abs/0912.5097
Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems
Autor:
Raphael, P., Rodnianski, I.
We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the S^2 target in all homotopy classes and for the critical equivariant SO(4) Yang-Mills problem. We derive sharp asymptotics on the dynamics at the blo
Externí odkaz:
http://arxiv.org/abs/0911.0692
Autor:
Klainerman, S., Rodnianski, I.
We give a geometric criterion for the breakdown of an Einstein vacuum space-time foliated by a constant mean curvature, or maximal, foliation. More precisely we show that the foliated space-time can be extended as long as the the second fundamental f
Externí odkaz:
http://arxiv.org/abs/0801.1709
Autor:
Klainerman, S., Rodnianski, I.
The paper is concerned with regularity properties of boundaries of causal pasts of points in a 3+1-dimensional Einstein-vacuum spacetime. In a Lorentzian manifold such boundaries play crucial role in propagation of linear and nonlinear waves. We prov
Externí odkaz:
http://arxiv.org/abs/math/0603010
Autor:
Klainerman, S., Rodnianski, I.
We propose a geometric construction of a first order physical space parametrix for solutions to covariant, tensorial wave equations on a curved background. We describe its applications to a large data breakdown criterion in General Relativity and als
Externí odkaz:
http://arxiv.org/abs/math/0603009
The focusing nonlinear Schrodinger equation possesses special non-dispersive solitary type solutions, solitons. Under certain spectral assumptions we show existence and asymptotic stability of solutions with the asymptoic profile (as time goes to inf
Externí odkaz:
http://arxiv.org/abs/math/0309114
We prove the dispersive estimates for charge transfer Hamiltonians, including the matrix non-selfadjoint generalizations. The charge transfer models appear naturally in the study of stability of multi-soliton systems.
Comment: 59 pages, 3 figure
Comment: 59 pages, 3 figure
Externí odkaz:
http://arxiv.org/abs/math/0309112
Autor:
Rodnianski, I., Schlag, W.
We establish dispersive and Strichartz estimates for solutions to the linear time-dependent Schr\"odinger equations with potential in three dimensions. Our main focus is on the small rough time-dependent potentials. Examples of such potentials are of
Externí odkaz:
http://arxiv.org/abs/math/0110098
Autor:
Klainerman, S., Rodnianski, I.
This is the third and last in our series of papers concerning rough solutions of the Einstein vacuum equations expressed relative to wave coordinates. In this paper we prove an important result concerning Ricci defects of microlocalized solutions, st
Externí odkaz:
http://arxiv.org/abs/math/0110090