Blowup behaviour for the nonlinear Klein--Gordon equation

Details Blowup behaviour for the nonlinear Klein--Gordon equation Blowup behaviour for the nonlinear Klein--Gordon equation

2012-03-22

arxiv.org/abs/1203.4886v1

Mathematics

Analysis of PDEs

Scientific paper

We analyze the blowup behaviour of solutions to the focusing nonlinear Klein--Gordon equation in spatial dimensions $d\geq 2$. 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.

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