Almost optimal local well-posedness for modified Boussinesq equations
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Date
2020-03-19
Authors
Geba, Dan-Andrei
Lin, Bai
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Modified Boussinesq equation, Well-posedness, Ill-posedness
Citation
Geba, 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.
Rights
Attribution 4.0 International