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);
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.
|Uncontrolled Keywords:||semi-linear wave equation, null condition, global existence, space-time L^2-estimate|
|Subjects:||35-xx PARTIAL DIFFERENTIAL EQUATIONS|