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