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arXiv:1909.03556 [math.AP]AbstractReferencesReviewsResources

A remark on norm inflation for nonlinear wave equations

Justin Forlano, Mamoru Okamoto

Published 2019-09-08Version 1

In this note, we study the ill-posedness of nonlinear wave equations (NLW). Namely, we show that NLW experiences norm inflation at every initial data in negative Sobolev spaces. This result covers a gap left open in a paper of Christ, Colliander, and Tao (2003) and extends the result by Oh, Tzvetkov, and the second author (2019) to non-cubic integer nonlinearities. In particular, for some low dimensional cases, we obtain norm inflation above the scaling critical regularity.

Comments: 15 pages
Categories: math.AP
Subjects: 35L05, 35B30
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