We study the low regularity well-posedness of the 1-dimensional cubic nonlinear fractional
Schr\" odinger equations with L\'{e} vy indices $1<\alpha< 2$. We consider both non …

We undertake a comprehensive study for the fractional nonlinear Schrödinger equation i∂<
sub> tu−(− Δ)< sup> su= μ< sub> 1| u|< sup> α1 u+ μ< sub> 2| u|< sup> α2 u, u (0)= u< sub> …

We prove a class of modified paraboloid restriction estimates with a loss of angular
derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes …

In this paper, we consider the Cauchy problem for the linear dispersive equations. We
establish the probabilistic radial Strichartz estimates for a randomization preserving the …

In this paper, we study the fractional Schrödinger equation in the Earth's gravitational field.
We firstly introduce a family of auxiliary functions to construct solutions to the fractional …

We prove a class of modified paraboloid restriction estimates with a loss of angular
derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes …

We consider the Cauchy problem for the critical fractional Schrödinger equation with the
power type nonlinearity. Hong-Sire [13] proved the local wellposedness, small data global …

We undertake a comprehensive study for the fractional nonlinear Schrödinger equation i∂
tu−(−∆) su= µ1| u| α1 u+ µ2| u| α2 u, u (0)= u0, where d 2d− 1≤ s< 1, 0< α1< α2< 4s d− 2s …

In this paper, the influence of the fractional dimensions of the L\'evy path under the Earth's
gravitational field is studied, and the phase transitions of energy and wave functions are …