\(L^p\) estimates for the wave equation with the inverse-square potential
The authors study the following linear wave equation \[ \begin{gathered} \square_n u+{a\over|x|^2} u= h(x,t),\\ u(x,0)= f(x),\\ \partial_t u(x,0)= g(x),\end{gathered}\tag{1} \] where \(\square_n= \partial^2_t- \Delta_n\) is the D'Alembertian in \(\mathbb{R}^{n+1}\) and \(a\) is a real number. They prove that Strichartz-type \(L^p\) estimates hold for solutions of the (1), under the additional assumption that the Cauchy data are spherically symmetric. Based on this estimate the authors prove global well-posedness in the critical norm for a nonlinear wave equation.
scientific article; zbMATH DE number 1890746