Renormalization and blow up for the critical Yang-Mills problem

Details Renormalization and blow up for the critical Yang-Mills problem Renormalization and blow up for the critical Yang-Mills problem

2008-09-11

arxiv.org/abs/0809.2114v2

Mathematics

Analysis of PDEs

59 pages

Scientific paper

We consider the Yangs-Mills equations in 4+1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are obtained by the spherically symmetric ansatz in the SO(4) gauge group and result by rescaling of the instanton solution. The rescaling is done via a prescribed rate which in this case is a modification of the self-similar rate by a power of |log t|. The powers themselves take any value exceeding 3/2 and thus form a continuum of distinct rates leading to blow-up. The methods are related to the authors' previous work on wave maps and the energy critical semi-linear equation. However, in contrast to these equations, the linearized Yang-Mills operator (around an instanton) exhibits a zero energy eigenvalue rather than a resonance. This turns out to have far-reaching consequences, amongst which are a completely different family of rates leading to blow-up (logarithmic rather than polynomial corrections to the self-similar rate).

Affiliated with

Also associated with

No associations

Rating

Renormalization and blow up for the critical Yang-Mills problem 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 Renormalization and blow up for the critical Yang-Mills problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Renormalization and blow up for the critical Yang-Mills problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-368563