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May/June 2019 Low regularity local well-posedness for the higher-dimensional Yang-Mills equation in Lorenz gauge
Hartmut Pecher
Adv. Differential Equations 24(5/6): 283-320 (May/June 2019). DOI: 10.57262/ade/1554256826

Abstract

We prove that the Yang-Mills equation in Lorenz gauge in the (n+1)-dimensional case, $n \ge 4$, is locally well-posed for data of the gauge potential in $H^s$ and the curvature in $H^r$, where $s > \frac{n}{2}-\frac{7}{8}$, $r > \frac{n}{2}-\frac{7}{4}$, respectively. The proof is based on the fundamental results of Klainerman-Selberg [7] and on the null structure of most of the nonlinear terms detected by Selberg-Tesfahun [16] and Tesfahun [19].

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Hartmut Pecher. "Low regularity local well-posedness for the higher-dimensional Yang-Mills equation in Lorenz gauge." Adv. Differential Equations 24 (5/6) 283 - 320, May/June 2019. https://doi.org/10.57262/ade/1554256826

Information

Published: May/June 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07197889
MathSciNet: MR3936012
Digital Object Identifier: 10.57262/ade/1554256826

Subjects:
Primary: 35L70 , 35Q40

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.24 • No. 5/6 • May/June 2019
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