In this paper, we investigate the long-time behavior of solutions to the two-dimensional Navier-Stokes equations with initial data evolving under the influence of the planar Couette flow. We focus on general perturbations, which may be large and of low regularity, including singular configurations such as point vortices, and show that the vorticity asymptotically approaches a constant multiple of the fundamental solution of the corresponding linearized vorticity equation after a long-time evolution determined by the relative Reynolds number.

Publication:

COMMUNICATIONS IN MATHEMATICAL PHYSICS

http://dx.doi.org/10.1007/s00220-026-05574-9

Author:Ning Liu

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

mail: liuning16@mails.ucas.ac.cn

Ping Zhang

State Key Laboratory of Mathematical Sciences, Academy of Mathematics & Systems Science, Beijing 100190, China.

mail: zp@amss.ac.cn

Weiren Zhao

Department of Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.

E-mail: zjzjzwr@126.com; wz19@nyu.edu