Ondes de gradients multidimensionnelles - 511

Recent techniques in partial differential equations have led to a solution to the general multidimensional Cauchy problem for nonlinear gradient waves.

In a blown-up configuration, Sable-Tougeron constructs a local solution for a quasilinear hyperbolic system with continuous Cauchy data, in which the first derivatives are discontinuous on a hyper surface.

This strong singularity is not so problematic as a rarefaction: The use of Alinhac's para-unknown leads to a tame inequality without loss of derivatives for the iterative scheme.