Global existence and decay rates of solutions to the viscous water-waves system. (November 2022)

• Record Type: Journal Article
• Authors: Bae, Hantaek; Lee, Woojae; Shin, Jaeyong
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: 35Q30 -- 35Q35 -- 76D27; Dias–Dyachenko–Zakharov model -- Viscous water-waves -- Global well-posedness -- Temporal decay rates; 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.2022.113062
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we analyze a nonlinear model of the viscous water-waves equation proposed in Dias et al. (2008). To this end, we first study the linear model in Dias et al. (2008). We then derive a new model which approximates the nonlinear model in Dias et al. (2008). We finally show the existence of a unique global-in-time solution and its decay rates to this new system with small initial data in energy spaces.