Regularity theory and global existence of small data solutions to semi-linear de Sitter models with power non-linearity. (April 2018)

• Record Type: Journal Article
• Authors: Ebert, M.R.; Reissig, M.
• Is Part Of: Nonlinear analysis. Volume 40(2018)
• Page Start: 14
• Page End: 54
• Publication Date: 2018-04
• Subjects: de Sitter model -- Power-nonlinearity -- Small data global existence -- Fractional chain rule -- Fractional Leibniz rule -- Fractional Gagliardo–Nirenberg inequality; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.08.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we consider the Cauchy problem for semi-linear de Sitter models with power non-linearity. The model of interest is ϕ t t − e − 2 t Δ ϕ + n ϕ t + m 2 ϕ = | ϕ | p, ( ϕ ( 0, x ), ϕ t ( 0, x ) ) = ( f ( x ), g ( x ) ), where m 2 is a non-negative constant. We study the global (in time) existence of small data solutions. In particular, we show the interplay between the power p, admissible data spaces and admissible spaces of solutions (in weak sense, in sense of energy solutions or in classical sense).