In this paper, we prove the global existence of analytic solution for 3D anisotropic Navier-Stokes system with initial data which is small and analytic in the vertical variable. We shall also prove that this solution will be analytic in the horizontal variables soon after t > 0. Furthermore, we show that the ratio between the analytic radius, Rh(t), of the solution in the horizontal variables and √t satisfies limt→0+ Rh(t) √t = ∞.

Publication:

Archive for Rational Mechanics and Analysis 

https://doi.org/10.1007/s00205-024-02051-2

Author:

N. Liu

Academy of Mathematics & Systems Science, The Chinese Academy of Sciences, Beijing 100190 China.

e-mail: liuning16@mails.ucas.ac.cn

P. Zhang

Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, The Chinese Academy of Sciences, Beijing 100190 China.

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049 China.

e-mail: zp@amss.ac.cn