Geodesic
Null structure and local well-posedness in the energy class for the Yang–Mills equations in Lorenz gauge
Journal of the European Mathematical Society, Tome 18 (2016) no. 8, pp. 1729-1752

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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 wellposedness 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 wellposedness 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 Hs×Hs–1-norm of the initial gauge potential, for some choice of s1 sufficiently close to 1.
DOI : 10.4171/jems/627
Classification : 35-XX
Keywords: Yang–Mills equations, well-posedness, Lorenz gauge, null structure 
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     author = {Sigmund Selberg and Achenef Tesfahun},
     title = {Null structure and local well-posedness in the energy class for the {Yang{\textendash}Mills} equations in {Lorenz} gauge},
     journal = {Journal of the European Mathematical Society},
     pages = {1729--1752},
     publisher = {mathdoc},
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     year = {2016},
     doi = {10.4171/jems/627},
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Sigmund Selberg; Achenef Tesfahun. Null structure and local well-posedness in the energy class for the Yang–Mills equations in Lorenz gauge. Journal of the European Mathematical Society, Tome 18 (2016) no. 8, pp. 1729-1752. doi: 10.4171/jems/627

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