The Cauchy problem for the dissipative Boussinesq equation. (February 2019)

• Record Type: Journal Article
• Authors: Wang, Shubin; Su, Xiao
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 116
• Page End: 141
• Publication Date: 2019-02
• Subjects: Cauchy problem -- Dissipative Boussinesq equation -- Global solutions -- Blow-up; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.06.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given.