Quantitative uniqueness estimates for the generalized non-stationary Stokes system
Quantitative uniqueness estimates for the generalized non-stationary Stokes system
复制标题
广义非平稳斯托克斯系统的定量唯一性估计
DOI：
10.1080/00036811.2020.1747611
复制
发表时间：
2020
影响因子：
1.1
通讯作者：
Jenn
中科院分区：
文献类型：
--
作者：
C. Lin;Jenn
本文研究一类具有奇异系数的广义非定常Stokes系统解的局部性态，其中。我们的主要结果之一是满足广义非平稳Stokes系统的非平凡解u的消失阶的一个界，它是u的（强）唯一连续性的一个定量形式.与已有的结果不同，我们的唯一延拓结果只涉及速度场u。我们的证明依赖于一些微妙的Carleman类型的估计。我们首先使用这些估计来导出u的关键最优三柱不等式。
ABSTRACT We study the local behavior of a solution to a generalized non-stationary Stokes system with singular coefficients in with . One of our main results is a bound on the vanishing order of a non-trivial solution u satisfying the generalized non-stationary Stokes system, which is a quantitative version of the (strong) unique continuation property for u. Different from the previously known results, our unique continuation result only involves the velocity field u. Our proof relies on some delicate Carleman-type estimates. We first use these estimates to derive crucial optimal three-cylinder inequalities for u.