# Blow-up and global solutions to L^p norm preserving non-local flows - Mathematics > Analysis of PDEs

Abstract: In this paper, we study global existence and blow up properties to $L^p$ normpreserving non-local heat flows. We first study two kinds of $L^p$ normpreserving non-local flows and prove that these flows have the globalsolutions. Finally, we give a example to show that one kind of this heat flowmay blow up in $L^{\infty}$ norm though its $L^p$ norm is preserved.

Author: Li Ma, Liang Cheng

Source: https://arxiv.org/