Quantitative uniqueness estimates for the generalized non-stationary Stokes system. Issue 10 (3rd July 2022)

• Record Type: Journal Article
• Authors: Lin, Ching-Lung; Wang, Jenn-Nan
• Is Part Of: Applicable analysis. Volume 101:Issue 10(2022)
• Page Start: 3591
• Page End: 3611
• Publication Date: 2022-07-03
• Subjects: Stokes system -- quantitative uniqueness estimates -- Carleman estimates; 35B60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1747611
• Languages: English
• ISSNs: 0003-6811

Abstract

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 .