Fractional nonlinear Schrödinger and Hartree equations in modulation spaces

Abstract

We establish global well-posedness for the mass subcritical nonlinear fractional Schrödinger equation $$i{u}_t-(-\Delta {)}^{\frac{\beta }{2}}u+F(u)=0$$ having radial initial data in modulation spaces $M^{p,\frac{p}{p-1}}({\mathbb{R}}^n)$ for $n\ge 2,p>2$ and $p$ sufficiently close to $2.$ The nonlinearity $F(u)$ is either of power-type $F(u)=\pm (|u{|}^{\alpha }u)(0<\alpha <2\beta /n)$ or Hartree-type $(|x{|}^{-\nu }\ast |u{|}^2)u(0<\nu <\min \{\beta ,n\}).$ Our order of dispersion $\beta$ lies in $(2n/(2n-1),2).$

24 pages. New results for Hartree equations added