ABSTRACT

We study the local behavior of a solution to a generalized non-stationary Stokes system with singular coefficients in $R^n$ with $n\ge 2$. 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.

中文翻译：

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广义非平稳斯托克斯系统的定量唯一性估计

摘要

我们研究了具有奇异系数的广义非平稳斯托克斯系统的解的局部行为$R^n$和$n\ge 2$. 我们的主要结果之一是满足广义非平稳斯托克斯系统的非平凡解u的消失顺序的界限，这是u的（强）唯一连续属性的定量版本。与之前已知的结果不同，我们独特的延拓结果仅涉及速度场u。我们的证明依赖于一些微妙的卡尔曼类型估计。我们首先使用这些估计来推导u的关键最优三缸不等式。