Strichartz estimates for wave equation with inverse square potential

Abstract

In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the range of admissible pairs is improved. As an application, we show the global well-posedness of the semi-linear wave equation with inverse-square potential ${\partial }_t^{2}u-\Delta u+\frac{a}{|x{|}^2}u=\pm |u{|}^{p-1}u$ for power $p$ being in some regime when the initial data are radial. This result extends the well-posedness result in Planchon, Stalker, and Tahvildar-Zadeh.

24pages

References in corpus (1)

• Angular Regularity and Strichartz Estimates for the Wave Equation

Cited by in corpus (6)

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• Linear adjoint restriction estimates for paraboloid
• Linear restriction estimates for Schroedinger equation on metric cones
• Price's law on Minkowski space in the presence of an inverse square potential
• Long time existence for semilinear wave equations with the inverse-square potential
• Scattering theory for nonlinear Schroedinger equations with inverse-square potential