Soichiro Katayama

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We consider wave equations in three space dimensions, and obtain new weighted L∞–L∞ estimates for a tangential derivative to the light cone. As an application, we give a new proof of the global existence theorem, which was originally proved by Klainerman and Christodoulou, for systems of nonlinear wave equations under the null condition. Our new proof has(More)
where Ω = R \ O, and O is a bounded open set in R with smooth boundary. Throughout this paper, we suppose that n is an odd integer with n ≥ 3. We assume that Ω is connected and that the initial data ~ f = (f0, f1) belongs to the associated energy space HD(Ω). Here and in the following, for an open set Y ⊂ R,HD(Y ) stands for the completion of (C 0 (Y )) 2(More)
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition(More)
The aim of this article is to present an elementary proof of a global existence result for nonlinear wave equations in an exterior domain. The novelty of our proof is to avoid completely the scaling operator which would make the argument complicated in the mixed problem, by using new weighted pointwise estimates of a tangential derivative to the light cone.
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