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Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge
We demonstrate null structure in the Yang-Mills equations in Lorenz gauge.
Such structure was found in Coulomb gauge by Klainerman and Machedon, who used
it to prove global well-posedness for finite-energy data. Compared with Coulomb
gauge, Lorenz gauge has the advantage---shared with the temporal gauge---that
it can be imposed globally in space even for large solutions. Using the null
structure and bilinear space-time estimates, we also prove local-in-time
well-posedness of the equations in Lorenz gauge, for data with finite energy.
The time of existence depends on the initial energy and on the -norm of the initial potential, for some .Comment: Minor typos corrected, references update