Ill-posedness results for generalized Boussinesq equations

2012/09/05 by Dan-Andrei Geba, Geba, Dan-Andrei, A. Alexandrou Himonas +3
Mathematics · Physics and Astronomy · #35B30 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1209.0998

openalex publication_date 2012/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we present ill-posedness results for generalized Boussinesq equations, which incorporate also the ones obtained by the authors for the classical "good" Boussinesq equation (arXiv:1202.6671). More precisely, we show that the associated flow map is not smooth for a range of Sobolev indices, thus providing a threshold for the regularity needed to perform a Picard iteration for these problems.

Citations

• Sharp local well-posedness for the "good" Boussinesq equation

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