# On the $L^{2}$-critical nonlinear Schrodinger equation with an inhomogeneous damping term

## TL;DR

This paper investigates the $L^{2}$-critical nonlinear Schrödinger equation with an inhomogeneous damping term, demonstrating the existence of global solutions and determining minimal blow-up times for certain initial data.

## Contribution

It establishes the existence of global solutions and quantifies minimal blow-up times for the inhomogeneous damped nonlinear Schrödinger equation.

## Key findings

- Existence of initial data leading to global solutions.
- Determination of minimal blow-up time for some initial data.
- Analysis of the effects of inhomogeneous damping on solution behavior.

## Abstract

We consider the $L^2$-critical nonlinear Schrodinger equation with an inhomogeneous damping term. We prove that there exists an initial data such that the corresponding solution is global in $H^1(R^d)$ and we give the minimal time of the blow up for some initial data.