9 papers
A paradox of the Navier-Stokes turbulence
Shijie Qin, Kun Xu, Shijun Liao
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/ar…
Spatial symmetry invariance of solution of Kolmogorov flow
Shijun Liao
We prove a mathematical theorem that solution for all of the two-dimensional (2D) Kolmogorov flow governed by Navier-Stokes (NS) equations with periodic boundary condition…
Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions
Shijun Liao, Shijie Qin
Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some…
Clean numerical simulation (CNS) of three-dimensional turbulent Kolmogorov flow
Shijie Qin, Shijun Liao
Turbulence holds immense importance across various scientific and engineering disciplines. The direct numerical simulation (DNS) of turbulence proposed by Orszag in 1970 is a miles…
Reply to the comments of McMullen et al. (arXiv:2510.04828)
Shijun Liao, Shijie Qin
McMullen et al. [1] comment that the numerical simulations that explicitly include random velocity fluctuations ``should exhibit a thermal-fluctuation-dominated range'' consistent…
Ultra-chaotic property of Navier-Stokes turbulence
Shijie Qin, Kun Xu, Shijun Liao
A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional tu…