Hokkaido Mathematical Journal

AZZOUZ J. E., IBRAHIM S.,

On the local solvability for a quasilinear cubic wave equation.

Hokkaido Mathematical Journal, 36 (2007) pp.383-416

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Abstract

This article is concerned with local solvability of the Cauchy problem for a quasilinear cubic wave equation in dimension $d=3$. Here, we improve the index of regularity of the initial data compared to the one given by classical energy methods.

MSC(Primary)20J05
MSC(Secondary)20C30
Uncontrolled Keywordsquasilinear wave equations, Strichartz estimates, energy method