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