Almost optimal local well-posedness for improved modified Boussinesq equations

2019/03/18 by Dan-Andrei Geba, Lin Bai, Geba, Dan-Andrei +1
Engineering · Mathematics · #35B30 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.07718

openalex publication_date 2019/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we investigate a class of improved modified Boussinesq equations, for which we provide first an alternate proof of local well-posedness in the space (H^s∩ L^∞)× (H^s∩ L^∞)(ℝ) (s≥ 0) to the one obtained by Constantin and Molinet. Secondly, we show that the associated flow map is not smooth when considered from H^s× H^s(ℝ) into H^s(ℝ) for s<0, thus providing a threshold for the regularity needed to perform a Picard iteration for these equations.

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