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A remark on the almost global existence theorems of Keel, Smith and Sogge

Preprint Series # 659
Hidano, Kunio and Yokoyama, Kazuyoshi A remark on the almost global existence theorems of Keel, Smith and Sogge. (2004);

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Abstract

We shall give a new proof of temporally global existence of small solutions for systems of semi-linear wave equations. Our proof uses the Klainerman-Sideris inequality and a space-time L^2-estimate. We shall also discuss whether the scale-invariant version of the space-time L^2-estimates can hold, and obtain some related estimates. Among other things, we prove that the Keel-Smith-Sogge estimate actually holds in all space dimensions.

Item Type:Preprint
Uncontrolled Keywords:semi-linear wave equation, null condition, global existence, space-time L^2-estimate
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:359
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