Local and Global Existence of A Nonlocal Equation with A Singular Integral Drift Term

TL;DR

This paper investigates the existence of solutions for a nonlocal fractional Laplacian equation with a singular drift, establishing conditions for both local and global solutions similar to previous studies.

Contribution

It extends existing results by proving local and global existence theorems for a nonlocal PDE with a singular drift term.

Findings

Established local existence of solutions.

Proved global existence under certain conditions.

Extended previous results to a nonlocal fractional setting.

Abstract

We study an initial value problem with fractional Laplacian and a singular drift term, and obtain local and global existence theorems similar to the results in Jourdain et al.(2005).