Global well-posedness of the two-dimensional Benjamin equation in the energy space. (February 2019)

• Record Type: Journal Article
• Authors: Chen, Wengu; Wei, Suqing; Li, Junfeng
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 755
• Page End: 788
• Publication Date: 2019-02
• Subjects: Benjamin equation -- Energy estimate -- Energy space -- Global well-posedness; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.08.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, the global well-posedness of the Cauchy problem for the two-dimensional Benjamin equation ∂ t u + ∂ x 3 u − ϵ H ∂ x 2 u − ∂ x − 1 ∂ y 2 u + ∂ x ( u 2 ∕ 2 ) = 0, u ( x, y, 0 ) = ϕ ( x, y ) in the energy space E 1 = { u : ‖ u ‖ L 2 + ‖ ∂ x u ‖ L 2 + ‖ ∂ x − 1 ∂ y u ‖ L 2 < ∞ } is obtained.