Blowup behaviour for the nonlinear Klein--Gordon equation
Analysis of PDEs
2012-03-23 v1
Abstract
We analyze the blowup behaviour of solutions to the focusing nonlinear Klein--Gordon equation in spatial dimensions . We obtain upper bounds on the blowup rate, both globally in space and in light cones. The results are sharp in the conformal and sub-conformal cases. The argument relies on Lyapunov functionals derived from the dilation identity. We also prove that the critical Sobolev norm diverges near the blowup time.
Cite
@article{arxiv.1203.4886,
title = {Blowup behaviour for the nonlinear Klein--Gordon equation},
author = {Rowan Killip and Betsy Stovall and Monica Visan},
journal= {arXiv preprint arXiv:1203.4886},
year = {2012}
}