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arXiv · 1909.03556

A remark on norm inflation for nonlinear wave equations

Justin Forlano·Mamoru Okamoto
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Abstract

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. We also prove ill-posedness for NLW, via norm inflation at general initial data, in negative regularity Fourier-Lebesgue and Fourier-amalgam spaces.

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Justin Forlano, Mamoru Okamoto. 2019-09-08. A remark on norm inflation for nonlinear wave equations. https://arxiv.org/abs/1909.03556

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