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Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge. (English) Zbl 1193.35164

Summary: It is known that the Maxwell-Klein-Gordon system (M-K-G), when written relative to the Coulomb gauge, is globally well-posed for finite-energy initial data. This result, due to Klainerman and Machedon, relies crucially on the null structure of the main bilinear terms of M-K-G in Coulomb gauge. It appears to have been believed that such a structure is not present in Lorenz gauge, but we prove here that it is, and we use this fact to prove finite-energy global well-posedness in Lorenz gauge. The latter has the advantage, compared to Coulomb gauge, of being Lorentz invariant, hence M-K-G in Lorenz gauge is a system of nonlinear wave equations, whereas in Coulomb gauge the system has a less symmetric form, as it contains also an elliptic equation.

MSC:

35Q40 PDEs in connection with quantum mechanics
35L70 Second-order nonlinear hyperbolic equations
81T13 Yang-Mills and other gauge theories in quantum field theory
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