We obtain the growth of Sobolev norms of the solution to the Maxwell–Dirac equations in R1+1 by applying elementary techniques. In particular, we estimate L∞ bound of the solution by making use of a local energy conservation. The similar idea can be applied to the Dirac–Klein–Gordon equations.

中文翻译：

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R1 + 1中Maxwell-Dirac和Dirac-Klein-Gordon系统的Sobolev范数的增长

通过应用基本技术，我们获得了R1 + 1中Maxwell-Dirac方程解的Sobolev范数的增长。特别地，我们通过利用局部能量守恒来估计解的L∞边界。类似的想法可以应用于Dirac–Klein–Gordon方程。