Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge

作者：Selberg Sigmund^*; Tesfahun Achenef

来源：Journal of the European Mathematical Society, 2016, 18(8): 1729-1752.

DOI：10.4171/JEMS/627

• Yang-Mills equations
• well-posedness
• Lorenz gauge
• null structure

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.

• 出版日期2016