We extend the results of Lebeau (2005) and Christ et al. (2007) to more general H1-supercritical nonlinearities. We also extend those results to the 2D case for exponentially growing nonlinearities. The proof uses the finite speed of propagation and a quantitative study of the associated O.D.E. It does not require any scaling invariance of the equation. To cite this article: S. Ibrahim et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).
ASJC Scopus subject areas