Geba, Dan-AndreiLin, Bai2021-09-212021-09-212020-03-19Geba, D. A., & Lin, B. (2020). Almost optimal local well-posedness for modified Boussinesq equations. <i>Electronic Journal of Differential Equations, 2020</i>(24), pp. 1-10.1072-6691https://hdl.handle.net/10877/14528In this article, we investigate a class of modified Boussinesq equations, for which we provide first an alternate proof of local well-posedness in the space (Hs ∩ L∞) x (Hs ∩ L∞)(ℝ) (s ≥ 0) to the one obtained by Constantin and Molinet [7]. Secondly, we show that the associated flow map is not smooth when considered from Hs x Hs(ℝ) into Hs(ℝ) for s < 0, thus providing a threshold for the regularity needed to perform a Picard iteration for these equations.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalModified Boussinesq equationWell-posednessIll-posednessArticle