Dispersive decay for the inter-critical nonlinear Schrödinger equation in R3

This paper investigates the Cauchy problem for the nonlinear Schrödinger equation (NLS) in the mass-supercritical and energy-subcritical regime within three spatial dimensions. For initial data in the critical homogeneous Sobolev space H ˙ s c ( R 3 ) (where s c = 5 6 ), we get a uniform decay estimate for the long-time dynamics of solutions, which extends the previous results.