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Ill-Posedness Issues on (abcd)-Boussinesq System
- Title
- Ill-Posedness Issues on (abcd)-Boussinesq System
- Authors
- Kwak C.; Maulén C.
- Ewha Authors
- 곽철광
- SCOPUS Author ID
- 곽철광
- Issue Date
- 2022
- Journal Title
- Journal of Dynamics and Differential Equations
- ISSN
- 1040-7294
- Citation
- Journal of Dynamics and Differential Equations
- Keywords
- abcd; BBM-BBM; Boussinesq system; Ill-posed; KdV-KdV
- Publisher
- Springer
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- In this paper, we consider the Cauchy problem for (abcd)-Boussinesq system posed on one- and two-dimensional Euclidean spaces. This model, initially introduced by Bona et al. (J Nonlinear Sci 12:283–318, 2002, Nonlinearity 17:925–952, 2004), describes a small-amplitude waves on the surface of an inviscid fluid, and is derived as a first order approximation of incompressible, irrotational Euler equations. We mainly establish the ill-posedness of the system under various parameter regimes, which generalize the result of one-dimensional BBM–BBM case by Chen and Liu (Anal Math 121:299–316, 2013). Among results established here, we emphasize that the ill-posedness result for two-dimensional BBM–BBM system is optimal. The proof follows from an observation of the high to low frequency cascade present in nonlinearity, motivated by Bejenaru and Tao (J Funct Anal 233:228–259, 2006). © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- DOI
- 10.1007/s10884-022-10189-4
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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