Remarks on the inhomogeneous fractional nonlinear Schrodinger equation

TL;DR

This paper investigates the well-posedness of the initial value problem for an inhomogeneous fractional nonlinear Schrödinger equation using a sharp Gagliardo-Nirenberg inequality.

Contribution

It introduces a new approach employing a sharp Gagliardo-Nirenberg inequality to analyze the well-posedness of the fractional inhomogeneous Schrödinger equation.

Findings

Established conditions for well-posedness

Derived new inequalities for fractional equations

Provided insights into the behavior of solutions

Abstract

Using a sharp Gagliardo-Nirenberg type inequality, well-posedness issues of the initial value problem for a fractional inhomogeneous Schrodinger equation are investigated.