Advances in Differential Equations

Low regularity local well-posedness for the higher-dimensional Yang-Mills equation in Lorenz gauge

Hartmut Pecher

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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].

Article information

Source
Adv. Differential Equations, Volume 24, Number 5/6 (2019), 283-320.

Dates
First available in Project Euclid: 3 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ade/1554256826

Mathematical Reviews number (MathSciNet)
MR3936012

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics 35L70: Nonlinear second-order hyperbolic equations

Citation

Pecher, Hartmut. Low regularity local well-posedness for the higher-dimensional Yang-Mills equation in Lorenz gauge. Adv. Differential Equations 24 (2019), no. 5/6, 283--320. https://projecteuclid.org/euclid.ade/1554256826


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