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Global solution to the two-dimensional Klein-Gordon equation. (English) Zbl 0741.35039
The existence of a global solution for the nonlinear Klein-Gordon equation is critical for the two-dimensional case. In this paper the authors prove global existence of solution for the nonlinear Klein-Gordon equation with small initial data in \(C_ 0^ \infty\). It is needed a sharp \(L^ \infty-L^ \infty\) estimate for the Cauchy problem involving the radial vector field \(L_ 0=t\partial_ t+x_ 1\partial_ 1+x_ 2\partial_ 2\).
Reviewer: A.Tsutsumi (Sakai)

MSC:
35L70 Second-order nonlinear hyperbolic equations
35Q40 PDEs in connection with quantum mechanics
35L15 Initial value problems for second-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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