3 citations · 7 across the 6 of their papers we have counts for
9 papers
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…
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…
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…
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…
Physical significance of artificial numerical noise in direct numerical simulation of turbulence
Shijun Liao, Shijie Qin
Using clean numerical simulation (CNS) in which artificial numerical noise is negligible over a finite, sufficiently long interval of time, we provide evidence, for the first time,…