Quantitative uniqueness estimates for the generalized non-stationary Stokes system. Issue 10 (3rd July 2022) - Lin, Ching-Lung; Wang, Jenn-Nan
ABSTRACT: We study the local behavior of a solution to a generalized non-stationary Stokes system with singular coefficients in R n with n ≥ 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 .