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Quasilinear wave equations and Strichartz estimates. (Équations d’ondes quasilinéaires et estimations de Strichartz.) (French) Zbl 0952.35073
The authors present an existence result for a certain class of quasilinear wave equations where the initial data are less regular than those required by energy methods. The main theorem is similar to a previous result established by G. Ponce and T. Sideris only for semilinear wave equations. The proof needs Strichartz estimates for wave operators whose coefficients are only Lipschitz continuous.
Reviewer: C.Popa (Iaşi)

MSC:
35L70 Second-order nonlinear hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L15 Initial value problems for second-order hyperbolic equations
35B45 A priori estimates in context of PDEs
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