2012/3/14 林景隆教授專題演講
演講者：
單 位：
日 期：2012年3月14日 PM 14:30
地 點：國立高雄大學理學院408室
講 題：
摘 要：
We study the local behavior of a solution to the Stokes system with singular coefficients in Rn 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 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.