Almost optimal local well-posedness for modified Boussinesq equations
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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 . 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.
CitationGeba, D. A., & Lin, B. (2020). Almost optimal local well-posedness for modified Boussinesq equations. Electronic Journal of Differential Equations, 2020(24), pp. 1-10.
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