粘性非线性波方程的规范膨胀

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-17 DOI:10.1007/s00030-024-00944-5

Pierre de Roubin, Mamoru Okamoto

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引用次数: 0

摘要

在这篇文章中，我们研究了粘性非线性波方程在负 Sobolev 空间中对任意多项式非线性的拟合不良性。特别是，我们证明了在某些情况下高于缩放临界正则性的规范膨胀结果。我们还证明了在某些正则性临界值以内，对于非线性的幂 k，\(C^k\)-连续性的失效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Norm inflation for the viscous nonlinear wave equation

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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Nonlinear Differential Equations and Applications (NoDEA)

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