5 papers
Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux
Sergiu Klainerman, Igor Rodnianski
The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucia…
Ricci defects of microlocalized Einstein metrics
S. Klainerman, I. Rodnianski
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 imp…
A physical space approach to wave equation bilinear estimates
Sergiu Klainerman, Igor Rodnianski, Terence Tao
Bilinear estimates for the wave equation in Minkowski space are normally proven using the Fourier transform and Plancherel's theorem. However, such methods are difficult to carry o…
Bilinear Estimates and Applications to Nonlinear Wave Equations
Sergiu Klainerman, Sigmund Selberg
We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assu…
On the Global Regularity of Wave Maps in the Critical Sobolev Norm
S. Klainerman, I. Rodnianski
We extend the recent result of T.Tao to wave maps defined from the Minkowski space of dimension >4 to a target Riemannian manifold which possesses a ``bounded parallelizable'' stru…