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

Fabrice Planchon; John G. Stalker; A. Shadi Tahvildar-Zadeh

doi:10.3934/dcds.2003.9.427

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2003, Volume 9, Issue 2: 427-442. Doi: 10.3934/dcds.2003.9.427

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

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

Received: September 30, 2001

Revised: February 28, 2002

Published: February 2003

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Abstract

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.

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Mathematics Subject Classification: 35L05, 35L15.

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