Speaker: Sirui Li, professor, School of Mathematics and Statistics, GuizhouUniversity

Date: December 9, 2023

Time: 10:00-11:30

Location: Tencent Meeting: 376 714 472

Sponsor: School of Mathematics, Shandong University

Abstract:

We consider a two-tensor hydrodynamics derived from the molecular model. Firstly, we prove the existence and uniqueness of local in time smooth solutions to the two-tensor system, Secondly, starting from the two-tensor hydrodynamics, by the Hilbert expansion we formally derive its biaixal limit, i.e., the frame hydrodynamics for the biaxial nematic phase, which is a coupled system between the evolution equation of the orthonormal frame field in SO(3) and the Navier-Stokes equation. Thirdly, for the biaxial hydrodynamics described by a field of othonormal frame, its well-posedness of smooth solutions in dimensional two and three and the global existence of weak solutions in dimensional two are shown, respectively. The uniqueness of global weak solutions is also established using the Littlewood-Paley theory. Finally, we rigorously justify the connection between the molecular-theory-based two-tensor hydrodynamics and the biaxial frame hydrodynamics. More specifically, we show the convergence of the solution to the two-tensor hydrodynamics to the solution to the frame hydrodynamics. This talk is based on joint works with Chenchen Wang (Guizhou University) and Jie Xu (ICMSEC, AMSSCAS).

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https://www.view.sdu.edu.cn/info/1020/186212.htm