Global sound waves for quasilinear second order wave equations (Q1322088)

The author studies the global existence of a class of sound waves (with small initial data) of quasilinear second order wave equations, namely of \(C^ 1\) solutions whose derivatives of order at least 2 are allowed to jump across a characteristic surface. General local existence results for sound waves have been obtained by Métivier. It is assumed that the space dimension is odd and at least equal to 3; using a conformal inversion, he then proves an extension to sound waves of global existence results (for smooth waves) due to Klainerman and Christodoulou. It is also shown that the global behaviour of sound waves strongly depends on the curvature properties of the surface across which their initial data are not \(C^ \infty\).