论文标题
Kiselev和Nazarov的主题变化：H {Ö} lder估计非本地运输扩散，沿着非无差异BMO领域
Variation on a theme by Kiselev and Nazarov: H{ö}lder estimates for non-local transport-diffusion, along a non-divergence-free BMO field
论文作者
论文摘要
我们证明，只要扩散的顺序在小尺度上占主导地位的传输项，我们就证明了具有分数扩散算子的传输扩散方程和BMO中的一般对流场的均匀的规律性估计；我们唯一的要求是在某些关键的Lebesgue空间中差异部分的小部分。与L.Silvestre（2012）的著名结果相比，我们的对流领域无需限制。如果对流场是连续的，则可以在超临界情况下获得类似的结果。我们的证明灵感来自A.Kiselev和F.Nazarov（2010），并基于双重演化技术。这个想法是在双重保护定律下传播原子特性（即在Lebesgue空间中的本地化和集成性），与分数扩散操作员相结合时。
We prove uniform Hölder regularity estimates for a transport-diffusion equation with a fractional diffusion operator,and a general advection field in BMO, as long as the order of the diffusion dominates the transport term at small scales;our only requirement is the smallness of the negative part of the divergence in some critical Lebesgue space. In comparison to a celebrated result by L.Silvestre (2012), our advection field does not need to be bounded. A similar result can be obtained in the super-critical case if the advection field is Hölder continuous. Our proof is inspired by A.Kiselev and F.Nazarov (2010) and is based on the dual evolution technique. The idea is to propagate an atom property (i.e. localization and integrability in Lebesgue spaces) under the dual conservation law, when it is coupled with the fractional diffusion operator.
