Dispersive decay for the nonlinear magnetic Schrödinger equation

Abstract

In this paper, we obtain the dispersive estimates and global well-posedness of the nonlinear magnetic Schrödinger equation in R3 with nonlinearity |u|p−1u with exponent 53<p<5 when the initial value stays in a suitable space Σs. By proving the resolvent estimates with weight functions and the “almost equivalence” between (−ΔA)s2 and (−Δ)s2, we obtain the Strichartz estimates of |JA(t)|su≔ei|x|24t(−t2ΔA)s2e−i|x|24tu, therefore the dispersive decay estimates are obtained.