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arXiv · 2308.07740

Norm inflation for the viscous nonlinear wave equation

Pierre de Roubin·Mamoru Okamoto
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Abstract

In this article, we study the ill-posedness of the viscous nonlinear wave equation for any polynomial nonlinearity in negative Sobolev spaces. In particular, we prove a norm inflation result above the scaling critical regularity in some cases. We also show failure of $C^k$-continuity, for $k$ the power of the nonlinearity, up to some regularity threshold.

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Pierre de Roubin, Mamoru Okamoto. 2023-08-15. Norm inflation for the viscous nonlinear wave equation. https://arxiv.org/abs/2308.07740

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