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引用次数: 0
摘要
本文引入保角巴赫流，并建立了它在闭流形上的适定性。我们也获得了它向后的独特性。为了尝试研究保角巴赫流的长期行为，假设曲率和压力函数是有界的，导出了曲率导数的全局和局部施型（L^2）估计。此外，使用\（L^2）-估计，并基于（Streets in Calc Var PDE 46:39–541013）中的一个想法，我们展示了施对曲率导数的逐点估计，而不假设Sobolev常数界。
In this article we introduce conformal Bach flow and establish its well-posedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type \(L^2\)-estimate of derivatives of curvatures is derived. Furthermore, using the \(L^2\)-estimate and based on an idea from (Streets in Calc Var PDE 46:39–54, 2013) we show Shi’s pointwise estimate of derivatives of curvatures without assuming Sobolev constant bound.
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