Dispersive decay for the nonlinear magnetic Schrödinger equation. (April 2022) - Wei, Lei; Duan, Zhiwen
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.