## Advances in Differential Equations

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

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

#### 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