演講公告
新聞標題： ( 2012-04-20 )
演講主題：Optimal three-ball inequalities and quantitative uniqueness for the Stokes system
主講人：林景隆 教授(成功大學 數學系)
演講日期：2012年4月24日(星期二) 下午2:00 –3:00
演講地點：(光復校區) 科學一館223室
茶會時間：當天下午1:30 (科學一館205室)
摘要內容：
We study the local behavior of a solution to the Stokes system with singular coefficients in $R^n$ with $n=2,3$. One of our main results is a bound on the vanishing order of a nontrivial solution $u$ satisfying the Stokes system, which is a quantitative version of the strong unique continuation property for $u$. Different from the previous known results, our strong 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 \emph{optimal} three-ball inequalities for $u$. Taking advantage of the optimality, we then derive an upper bound on the vanishing order of any nontrivial solution $u$ to the Stokes system from those three-ball inequalities. As an application, we derive a minimal decaying rate at infinity of any nontrivial $u$ satisfying the Stokes equation under some a priori assumptions.
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