L^p Estimates for the wave equation with the inverse-square potential

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March 2003, 9(2): 427-442. doi: 10.3934/dcds.2003.9.427

$L^p$ Estimates for the wave equation with the inverse-square potential

Fabrice Planchon ^1, , John G. Stalker ^2, and A. Shadi Tahvildar-Zadeh ^3,

1.	Laboratoire d'Analyse Numérique, URA CNRS 189, Université Pierre et Marie Curie, 175 rue Chevaleret, 75252 Paris, France
2.	Department of Mathematics, Princeton University, Princeton N.J. 08544, United States
3.	Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway NJ 08854, United States

Received October 2001 Revised March 2002 Published December 2002

Abstract
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We prove that Strichartz-type $L^p$ estimates hold for solutions of the linear wave equation with the inverse square potential, under the additional assumption that the Cauchy data are spherically symmetric. The estimates are then applied to prove global well-posedness in the critical norm for a nonlinear wave equation.

Keywords: inverse-square potential, conjugation operator., space-time estimates, Wave equation.

Mathematics Subject Classification: 35L05, 35L1.

Citation: Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. $L^p$ Estimates for the wave equation with the inverse-square potential. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 427-442. doi: 10.3934/dcds.2003.9.427

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