Sharp Global Existence for Semilinear Wave Equation with Small Data

Abstract

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

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

References in corpus (1)

• Ill-Posedness for Semilinear Wave Equations with Very Low Regularity

Cited by in corpus (1)

• Ill-Posedness for Semilinear Wave Equations with Very Low Regularity