论文标题
传播运输方程的规律性。 Littlewood-Paley方法
Propagation of regularity for transport equations. A Littlewood-Paley approach
论文作者
论文摘要
众所周知，具有SOBOLEV速度场的线性对流方程的规律性非常差：溶液仅传播对数顺序的衍生物，该衍生物可以根据合适的Gagliardo seminors进行测量。我们提出了一种基于Littlewood-Paley理论的规律研究的新方法，从而衡量了BESOV规范的规律性。我们恢复文献中可用的结果，并最佳地扩展到扩散设置。结果，我们在零扩散率极限中的收敛速率得出了急剧的界限。
It is known that linear advection equations with Sobolev velocity fields have very poor regularity properties: Solutions propagate only derivatives of logarithmic order, which can be measured in terms of suitable Gagliardo seminorms. We propose a new approach to the study of regularity that is based on Littlewood-Paley theory, thus measuring regularity in terms of Besov norms. We recover the results that are available in the literature and extend these optimally to the diffusive setting. As a consequence, we derive sharp bounds on rates of convergence in the zero-diffusivity limit.
