Concerning the pathological set in the context of probabilistic well-posedness
arXiv:2001.10293
Abstract
We prove a complementary result to the probabilistic well-posedness for the nonlinear wave equation. More precisely, we show that there is a dense set of the Sobolev space of super-critical regularity such that (in sharp contrast with the probabilistic well-posedness results) the family of global smooth solutions, generated by the convolution with some approximate identity of the elements of , does not converge in the space of super-critical Sobolev regularity.
arXiv commentIn this version, we add a further consequence (Corollary 1.2) of the main result and correct a small error, compared to the article appeared in: Comptes Rendus Mathematique, Vol. 358, issue 9-10 (2020), p. 989-999