Well-posedness and scattering of small amplitude solutions to Boussinesq paradigm equation. (August 2019)

• Record Type: Journal Article
• Authors: Liu, Guowei; Wang, Weike
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 141
• Page End: 160
• Publication Date: 2019-08
• Subjects: Boussinesq paradigm equation -- Well-posedness -- Scattering -- Dispersive estimate -- Oscillatory integral -- Bessel function; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper studies the existence and scattering of global small amplitude solutions to the nonlinear Boussinesq paradigm equation in R n . Firstly, with a dispersive estimate obtained by oscillatory integral and some properties of Bessel function, the existence of global small amplitude solutions is established by the method of contractive mapping principle. Then, with the help of the decay of solutions with respect to time, we construct the suitable scattering state corresponding to the small amplitude solutions.