Workshop on some aspects of incompressible
Date: March 21 & 22, 2018
Venue: Room 1124, New main building, BNU
Mikhail Korobkov (Fudan U)
Zhen Lei (Fudan U)
Yanyan Li (Rutgers U. & BNU)
Gregory Seregin (U. Oxford)
Jiahong Wu (Oklahoma State U)
Ping Zhang (AMSS, CAS)
Zhifei Zhang (PKU)
Yanyan Li (Co-Chair), Jingang Xiong (Co-Chair, Email: firstname.lastname@example.org)
Jiguang Bao, Haigang Li, Zhongwei Tang, Xiaojing Xu
10:00—11:00, Gregory Seregin
11:00—12:00, Ping Zhang
14:00—15:00, Jiahong Wu
15:00—16:00, Yanyan Li
9:00—10:00, Zhifei Zhang
10:00—11:00, Zhen Lei
11:10—12:10, Mikhail Korobkov
Titles & Abstracts:
Mikhail Korobkov: On convergence of arbitrary D-solution of steady Navier--Stokes system in 2D exterior domains
Abstract: This is a new joint work with K.Pileckas and R.Russo. We study solutions to stationary Navier--Stokes system in two dimensional exterior domains. We prove that any such solution with finite Dirichlet integral converges to a constant vector at infinity uniformly. No additional condition (on symmetry or smallness, etc.) are assumed. The proofs based on arguments of the classic Amick's article (Acta Math., 1988) and on results of recent papers by authors where the uniform boundedness of these solutions was established.
Zhen Lei：Sharp One Component Regularity for Navier-Stokes
Abstract: In this talk we will first present that one component of velocity has an a priori bound which is critical with respect to the natural scaling of Navier-Stokes in the axi-symmetric case. We then turn to present the study on one component regularity for Navier-Stokes equations. Certain criticality property of the axi-symmetric Navier-Stokes equations will also be reported.
Yanyan Li：Homogeneous axisymmetric solutions of incompressible stationary
Navier-Stokes equations and vanishing viscosity limit
Abstract: We present results on the existence of (-1)-homogeneous axisymmetric solutions of incompressible stationary Navier-Stokes equations which are smooth on the unit sphere minus the north and south poles. In particular we classify such solutions with no swirl, and analyze their limiting behavior as viscosity tends to zero.
Jiahong Wu: Stability and regularity results for the 2D Boussinesq equations with partial dissipation
Abstract: This talk presents recent work on the stability problem concerning two equilibrium solutions to the 2D Boussinesq equations with partial dissipation. First, we describe the linear and nonlinear stability results on the hydrostatic equilibrium of the 2D Boussinesq equations with only velocity dissipation. Second, we explain results on the stability of the Couette flow for the 2D Boussinesq equations with vertical dissipation.
Ping Zhang: TBA
Zhifei Zhang: Enhanced dissipation and transition threshold for Kolmogorov flow and Couette flow