Quasilinear wave equations and Strichartz estimates. (Équations d’ondes quasilinéaires et estimations de Strichartz.) (French) Zbl 0952.35073

Bahouri, Hajer; Chemin, Jean-Yves

Am. J. Math. 121, No. 6, 1337-1377 (1999).

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

Keywords:

Lipschitz continuous coefficients