具有稳定初值的无粘Burgers方程正则点的豪斯多夫维数
On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data
摘要：
考虑一个无粘Burgers方程，其初始数据是一个Levy a-稳定过程Z，且a > 1。我们证明了当Z有正跳时，当a接近1时，与方程相关的拉格朗日正则点集的豪斯多夫维数严格小于1/a.这对Janicki和Woyczynski的一个猜想给出了否定的回答。在此过程中，我们反驳了Z. Shi关于积分稳定过程的下尾.
英文摘要：
Consider an inviscid Burgers equation whose initial data is a Levy a-stable process Z with a > 1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller than 1/a, as soon as a is close to 1. This gives a negative answer to a conjecture of Janicki and Woyczynski. Along the way, we contradict a recent conjecture of Z. Shi about the lower tails of integrated stable processes.
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