Well-posedness of a highly nonlinear shallow water equation on the circle. (August 2020)

• Record Type: Journal Article
• Authors: Duruk Mutlubas, Nilay; Geyer, Anna; Quirchmayr, Ronald
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: primary 35Q35 -- secondary 35L30; Shallow water equation -- Large amplitude waves -- Cubic nonlinearity -- Well-posedness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111849
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space H s on the circle for s > 3 ∕ 2 .