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

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  • 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].

    Mathematics Subject Classification: 35Q40, 35L70.


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