Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume 18, Issue 8, Pages 1729-1752Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JEMS/627
Keywords
Yang-Mills equations; well-posedness; Lorenz gauge; null structure
Categories
Funding
- Research Council of Norway [213474/F20]
Ask authors/readers for more resources
We demonstrate null structure in the Yang-Mills equations in Lorenz gauge. Such structure was found in Coulomb gauge by Klainerman and Machedon, who used it to prove global well-posedness for finite-energy data in the temporal gauge by passing to local Coulomb gauges via Uhlenbeck's Lemma. Compared with the Coulomb gauge, the Lorenz gauge has the advantage-shared with the temporal gauge-that it can be imposed globally in space even for large solutions. Using the null structure and bilinear space-time estimates, we also prove local-in-time well-posedness of the Yang-Mills equations in Lorenz gauge for data with finite energy, with a time of existence depending on the initial energy and on the H-s x Hs-1-norm of the initial gauge potential, for some choice of s < 1 sufficiently close to 1.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available