Long-Time Existence for Small Amplitude Semilinear Wave Equations

We prove that a certain class of semilinear wave equations has global solutions if the initial data is small. These existence results rely on mixed-norm angular-radial space-time estimates. More specifically, we consider power nonlinearities, $\square u=F_{p}(u)$, where $F_{p}(u)\sim |u|^{p}$ and $\...

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Veröffentlicht in:	American journal of mathematics 1996-10, Vol.118 (5), p.1047-1135
Hauptverfasser:	Lindblad, Hans, Sogge, Christopher D.
Format:	Artikel
Sprache:	eng
Schlagworte:	Cauchy problem Existence theorems Mathematical integrals Mathematics Sine function Spatial dimensions Spherical coordinates Spherical harmonics Uniqueness Wave equations
Online-Zugang:	Volltext
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