Sharp Global Existence for Semilinear Wave Equation with Small Data

Details Sharp Global Existence for Semilinear Wave Equation with Small Data Sharp Global Existence for Semilinear Wave Equation with Small Data

2006-12-10

arxiv.org/abs/math/0612249v3

Mathematics

Analysis of PDEs

4 pages, version 3, the sharpness for the result is explained

Scientific paper

By using the Strichartz esitmate and Picard iteration, we prove the subcritical(critical in some cases) global solution in $C_t H_x^s\cap C_t^1 H^{s-1}_x$ with small data for semilinear wave equation with nonlinearity of type $(\partial u)^k$($k\ge 1+\frac{4}{n-1}\vee 2$ and $(n,k)\neq (3,3)$). For $(n,k)=(3,3)$, we get the almost global existence. In addition, we give the global existence with radial data when $k> 1+\frac{2}{n-1}\vee 2$.

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