Stability of solutions for nonlinear Schrödinger equations in critical spaces

Abstract

We consider the Cauchy problem for nonlinear Schrodinger equation iut + Δu = ± |u|pu, \(\frac{4} {d} < p < \frac{4} {{d - 2}}\) in high dimensions d ⩾ 6. We prove the stability of solutions in the critical space \(\dot H_x^{s_p }\), where \(s_p = \frac{d} {2} - \frac{2} {p}\).