Dispersive decay for the nonlinear magnetic Schrödinger equation. (April 2022)

• Record Type: Journal Article
• Authors: Wei, Lei; Duan, Zhiwen
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: 35B40 -- 35Q41 -- 35Q55 -- 81Q20; Nonlinear magnetic Schrödinger equation -- Dispersive decay -- Resolvent estimates -- Strichartz estimates; 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.2021.112743
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we obtain the dispersive estimates and global well-posedness of the nonlinear magnetic Schrödinger equation in R 3 with nonlinearity | u | p − 1 u with exponent 5 3 < p < 5 when the initial value stays in a suitable space Σ s . By proving the resolvent estimates with weight functions and the "almost equivalence" between ( − Δ A ) s 2 and ( − Δ ) s 2, we obtain the Strichartz estimates of | J A ( t ) | s u ≔ e i | x | 2 4 t ( − t 2 Δ A ) s 2 e − i | x | 2 4 t u, therefore the dispersive decay estimates are obtained.