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Low regularity local solutions for field equations. (English) Zbl 0852.35098
Summary: We prove local existence and uniqueness of low regularity solutions to semilinear systems of coupled wave equations and of coupled Dirac-Klein-Gordon equations. The smoothness of our solutions is below the classical level. The main lemma is an \(L^2\) estimate for products of solutions of linear equations inspired by earlier work by Strichartz, Klainerman and Machedon.

MSC:
35L70 Second-order nonlinear hyperbolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35L55 Higher-order hyperbolic systems
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