Abstract In this article, we focus on the uniqueness question for (expanding) solutions of the harmonic map flow coming out of smooth 0-homogeneous maps with values into a closed Riemannian manifold. We introduce a relative entropy for two purposes. On the one hand, we prove the existence of two expanding solutions associated to any suitable solution coming out of a 0-homogeneous map by a blow-up and a blow-down process. On the other hand, generic uniqueness of expanding solutions coming out of the same 0-homogeneous map of 0 relative entropy is proved.

中文翻译：

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谐波映射流扩展器的相对熵

摘要 在本文中，我们关注从具有值的平滑 0-齐次映射到闭合黎曼流形的谐波映射流的（扩展）解的唯一性问题。我们引入相对熵有两个目的。一方面，我们证明了两个扩展解的存在，这两个扩展解与通过吹胀和吹灭过程从 0 齐次映射中产生的任何合适的解相关。另一方面，证明了来自相同的 0 相对熵的 0 齐次映射的扩展解的通用唯一性。