# The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity

## TL;DR

This paper studies the heat equation with fractional Laplacian and exponential nonlinearity, establishing local and global solutions, and decay estimates in Lebesgue spaces, advancing understanding of such equations in functional analysis.

## Contribution

It introduces local well-posedness results in Orlicz spaces and proves global existence for small initial data for the fractional heat equation with exponential nonlinearity.

## Key findings

- Local well-posedness in Orlicz spaces
- Global solutions for small initial data
- Decay estimates in Lebesgue spaces

## Abstract

We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We obtain decay estimates for large time in Lebesgue spaces.