Scattering threshold for the focusing nonlinear Klein-Gordon equation

Details Scattering threshold for the focusing nonlinear Klein-Gordon equation Scattering threshold for the focusing nonlinear Klein-Gordon equation

2010-01-10

arxiv.org/abs/1001.1474v3

Mathematics

Analysis of PDEs

56 pages, no figure, minor corrections, to appear in Analysis & PDE

Scientific paper

We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig-Merle for the $H^1$ critical wave and Schr\"odinger equations. Our result includes the $H^1$ critical case, where the threshold is given by the ground state for the massless equation, and the 2D square-exponential case, where the mass for the ground state may be modified, depending on the constant in the sharp Trudinger-Moser inequality. The main difficulty is lack of scaling invariance both in the linear and nonlinear terms.

Affiliated with

Also associated with

No associations

Rating

Scattering threshold for the focusing nonlinear Klein-Gordon equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scattering threshold for the focusing nonlinear Klein-Gordon equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scattering threshold for the focusing nonlinear Klein-Gordon equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-128170