Abstract
Consider a quasi-linear system of two Klein–Gordon equations with masses m 1, m 2. We prove that when m 1≠2 m 2 and m 2≠2 m 1, such a system has global solutions for small, smooth, compactly supported Cauchy data. This extends a result proved by Sunagawa (J. Differential Equations 192 (2) (2003) 308) in the semi-linear case. Moreover, we show that global existence holds true also when m 1=2 m 2 and a convenient null condition is satisfied by the nonlinearities.
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