Infinite energy solutions for the (3+1)-dimensional Yang-Mills equation in Lorenz gauge

Hartmut Pecher

doi:10.3934/cpaa.2019033

Article Contents

2019, Volume 18, Issue 2: 663-688. Doi: 10.3934/cpaa.2019033

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Infinite energy solutions for the (3+1)-dimensional Yang-Mills equation in Lorenz gauge

Hartmut Pecher

Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany

Received: December 2017

Revised: May 2018

Published: October 2018

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Abstract

We prove that the Yang-Mills equation in Lorenz gauge in the (3+1)-dimensional case is locally well-posed for data of the gauge potential in $H^s$ and the curvature in $H^r$, where $s >\frac{5}{7}$ and $r > -\frac{1}{7}$, respectively. This improves a result by Tesfahun [16]. The proof is based on the fundamental results of Klainerman-Selberg [6] and on the null structure of most of the nonlinear terms detected by Selberg-Tesfahun [14] and Tesfahun [16].

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Mathematics Subject Classification: 35Q40, 35L70.

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References

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