Lucente, Sandra Nonlinear wave equation with potential. (English) Zbl 0979.35103 Tsukuba J. Math. 24, No. 1, 81-107 (2000). The author proves the existence of a unique global solution of the Cauchy problem for the equation \(u_{tt}-\triangle u+V(x)|u|^{p-1}u=0\) \((x\in \mathbb{R}^{n}\), \(t>0)\), where \(V(x)=|x-x_{0}|\) for \(n=3\), or \(V(x)>0\) for \(n>3\), and \(p\) is a subcritical or critical exponent. To prove it, she uses Satah-Struwe technique and proves weighted nonlinear estimates in Besov spaces. Reviewer: Marie Kopáčková (Praha) MSC: 35L70 Second-order nonlinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations 35B45 A priori estimates in context of PDEs Keywords:semilinear wave equation; Besov spaces; Strichartz estimate; Satah-Struwe technique; weighted nonlinear estimates PDFBibTeX XMLCite \textit{S. Lucente}, Tsukuba J. Math. 24, No. 1, 81--107 (2000; Zbl 0979.35103) Full Text: DOI