From the 1 of 7 linked papers with an AI index.
7 papers
Inevitable shock formation for 3-D compressible Euler flows
Sergiu Klainerman, Qian Wang, Shiwu Yang +1
We prove that solutions arising from smooth, sufficiently small, compactly supported perturbations of non-vacuum constant states in three-dimensional irrotational compressible flow…
Formation of Trapped Surfaces from Spacelike Initial Data
Xuantao Chen, Sergiu Klainerman
The paper constructs specific short‑pulse spacelike initial data for Einstein’s equations and shows how these data can be extended to asymptotically flat Cauchy data, leading to th…
A Physical space derivation of Morawetz-Energy estimates in Kerr spacetimes with large angular momentum
Lili He, Sergiu Klainerman
We revisit the derivation of Morawetz--energy estimates for scalar wave equations in the domain of outer communication of a Kerr spacetime \(\KK(a,m)\). Our goal is to develop robu…
Forward Construction of Vacuum Initial Data with Borderline Decay
Xuantao Chen, Sergiu Klainerman
We make use of the free data formalism developed in \cite{CK25} to construct solutions of the Einstein vacuum constraint equations by integrating in the forward direction. This, to…
Solving the constraint equation for general free data
Xuantao Chen, Sergiu Klainerman
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical…
Decay estimates of wave equations in un-isotropic media
Sergiu Klainerman, Xuecheng Wang
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation proper…