Global Well-posedness for an incompressible flow with intrinsic degrees of freedom in bounded domains. Issue 6 (26th April 2017)

• Record Type: Journal Article
• Authors: Zhou, Daoguo
• Is Part Of: Applicable analysis. Volume 96:Issue 6(2017)
• Page Start: 1004
• Page End: 1015
• Publication Date: 2017-04-26
• Subjects: Well-posedness -- Navier–Stokes equations -- intrinsic degrees of freedom -- weak–strong uniqueness; 35Q35 -- 76D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1169530
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider a mathematical model for an incompressible Newtonian fluid with intrinsic degrees of freedom in a smooth bounded domain. We first show that there exists a unique local strong solution for large initial data. Then, we prove that the local strong solution is indeed global provided that the initial data is sufficiently small. Furthermore, we prove that when the strong solution exists, all the global weak solutions constructed by Lions must be equal to the unique strong solution with the same initial data.