Blow-up and global solutions to L^p norm preserving non-local flows

Li Ma; Liang Cheng

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arXiv · 0910.4788

Blow-up and global solutions to L^p norm preserving non-local flows

Li Ma·Liang Cheng

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Abstract

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.

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Li Ma, Liang Cheng. 2009-10-26. Blow-up and global solutions to L^p norm preserving non-local flows. https://arxiv.org/abs/0910.4788

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