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

2012/03/28 by Nobu Kishimoto, Kishimoto, Nobu · 1 citation
Mathematics · #35Q55 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1203.6374

openalex publication_date 2012/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present article, we prove the sharp local well-posedness and ill-posedness results for the "good" Boussinesq equation on \mathbbT; the initial value problem is locally well-posed in H^-1/2(\mathbbT) and ill-posed in H^s(\mathbbT) for s-3/8 given by Oh and Stefanov (2012) to the regularity threshold H^-1/2(\mathbbT). Similar ideas also establish the sharp local well-posedness in H^-1/2(ℝ) and ill-posedness below H^-1/2 for the nonperiodic case, which improves the result of Tsugawa and the author (2010) in H^s(ℝ) with s>-1/2 to the limiting regularity.

Citations

• Some local wellposedness results for nonlinear Schroedinger equations below L²
• Sharp ill-posedness results for the KdV and mKdV equations on the torus
• Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation

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• Ill-posedness results for generalized Boussinesq equations

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