Liyuan Distinguished Scholar twenty-three: Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain

Title: Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain

Speaker: Prof. Ping Zhang, Academician of Chinese Academy of Sciences (Academy of Mathematics and Systems Sciences)

Lecture time: March 24, 2024 (Sunday) 14:00-15:00

Lecture location: No. 3 Lecture Hall of Huixing Building, Yuehai Campus, SZU

Overview: In this talk, we first present the global existence and stability of solutions to 3-D classical Navier-Stokes equations $(NS)$ in an infinite cylindrical domain with large Fourier mode initial data. Then we extend similar result for 3-D anisotropic Navier-Stokes equations $(ANS).$ We remark that due to the loss of vertical viscosity in $(ANS),$ the construction of the energy functionals for $(ANS)$ is much more subtle than that of $(NS).$ Compared with our previous paper for $(NS)$, we improve the polynomial decay in $k$ for the Fourier coefficients of the solution to be exponential decay in $k$ here.

Speaker Introduction: Prof. Ping Zhang currently serves as the Director and Legal Representative of the Institute of Mathematics and Systems Science at the Chinese Academy of Sciences (CAS), and is an Academician of the CAS. He earned his bachelor's degree from Nanjing University in 1991 and his Ph.D. from the same university in 1997. From 1997 to 1999, he completed his postdoctoral research at the Institute of Mathematics, CAS. He then served as an Assistant Researcher at the Institute of Mathematics and Systems Science, CAS, from 1999 to 2001, and as an Associate Researcher from 2001 to 2003. Since 2003, he has been a Researcher at the Institute. Zhang has received several prestigious awards, including the National Science Fund for Distinguished Young Scholars in 2005, the Tenth China Youth Science and Technology Award in 2007, the Second Class National Natural Science Award in 2011, and the Changjiang Distinguished Professorship under the Ministry of Education's Key Talent Program (at the University of the Chinese Academy of Sciences) in 2014. In 2019, he was honored with the Chern Medal Award by the Chinese Mathematical Society, and in 2021, he was elected as an Academician of the Chinese Academy of Sciences.

Teachers and students are welcome to participate!

Invited by: School of Mathematical Sciences

School of Mathematical Sciences

March 12, 2024