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DISCRETE AND CONTINUOUS Website: DYNAMICAL SYSTEMS Volume , Number 0, Xxxx 2001 pp. 000{000 L p ESTIMATES FOR THE WAVE EQUATION WITH THE INVERSE-SQUARE POTENTIAL Fabrice Planchon Laboratoire d'Analyse Numerique, URA CNRS 189 Universite Pierre et Marie Curie, 175 rue Chevaleret, 75252 Paris, France John G. Stalker Department of Mathematics Princeton University, Princeton NJ 08544 A. Shadi Tahvildar-Zadeh Department of Mathematics, Rutgers, The State University of New Jersey 110 Frelinghuysen Road, Piscataway NJ 08854 Abstract. We prove that Strichartz-type L p estimates hold for solutions of the lin- ear 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. 1. Introduction. Consider the following linear wave equation 8 < : n u+ a jxj 2 u = h(x; t) u(0; x) = f(x) @ t u(0; x) = g(x) (1.1) where n = @ 2 t n is the D'Alembertian in R n+1 and a is a real number.

wave equation

conjugation operator

estimates hold

given any

any strip

smooth functions

maxrel

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Publié par

pefav

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