Xuefeng Liu, Professor, Tokyo Woman's Christian University, Japan

Shuo Zhang, Associate Professor

Some problems in solution verification for the Navier-Stokes equations

10:00-11:00 December 27(Friday), Z301

Recently, verified computation has emerged as a powerful tool for providing explicit error estimates for numerical solutions to boundary value and eigenvalue problems of differential operators. The author’s recent book [1] surveys these developments, showcasing significant progress in the field. In this talk, I will summarize the latest results on verified computation, with a focus on spectral problems and solution verification for the Navier-Stokes equations [2].

Additionally, I will outline the objectives of an ongoing project aimed at verifying the existence of multiple solutions to the Navier-Stokes equations in 3D domains. This discussion will highlight several key challenges associated with this goal.

References:

[1] Xuefeng LIU, Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems, Springer Singapore, July 2024.

[2] Xuefeng Liu, Mitsuhiro T. Nakao, Shin’ichi Oishi, Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains, Communications in Nonlinear Science and Numerical Simulation, Volume 108, 2022, 106223.