Academic Report of School of Mathematical Sciences [2026] No. 056

(Series Report for High-Level University Construction No. 1315)

Title：Global well-posedness of 2-D incompressible anisitropic Navier-Stokes equations with variable density

Speaker：Guilong Gui, Professor (Xiangtan University)

Time：10:00-11:00, June 17, 2026

Location：Huixing Building Room 514, Yuehai Campus

Abstract: We investigate the global well-posedness of two-dimensional inhomogeneous incompressible anisotropic Navier–Stokes systems, assuming the initial density is bounded away from zero and infinity. For the (AINS) system (with partial dissipation) on $\mathbb{R}^2$, we prove existence and uniqueness of global solutions for finite-energy initial data using time-weighted energy estimates and a duality argument. For the (HINS) system (with only horizontal dissipation) on $\mathbb{T} \times \mathbb{R}$, global well-posedness is established provided the initial velocity and density variation are sufficiently small.

Speaker Profile：Guilong Gui is a professor and doctoral advisor at the School of Mathematics and Computational Science, Xiangtan University. He received his Ph.D. in Pure Mathematics from the Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, in 2010. In 2011, he was awarded the Zhong Jiaqing Mathematics Prize by the Chinese Mathematical Society. His research focuses on the mathematical theory of fluid dynamics equations, covering topics such as the well-posedness and stability of the inhomogeneous incompressible Navier-Stokes equations and related models, free boundary problems in fluid dynamics, and the semiclassical limit theory of the nonlinear Schrödinger equation. His papers have been published in international mathematical journals including CPAM, CMP, ARMA, Adv. Math., CPDE, JMPA, and JFA.

Faculty and students are welcome to attend!

Invited by: Qingtian Zhang

School of Mathematical Sciences

June 11, 2026