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Asymptotic behavior and time discretization analysis for the non-stationary Navier-Stokes problem

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Summary.

The asymptotic behavior and the Euler time discretization analysis are presented for the two-dimensional non-stationary Navier-Stokes problem. If the data ν and f(t) satisfy a uniqueness condition corresponding to the stationary Navier-Stokes problem, we then obtain the convergence of the non-stationary Navier-Stokes problem to the stationary Navier-Stokes problem and the uniform boundedness, stability and error estimates of the Euler time discretization for the non-stationary Navier-Stokes problem.

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Acknowledgments.

We would like to thank all referees for their useful suggestions and comments which have improved this paper.

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Authors and Affiliations

  1. Faculty of Science(State Key Laboratory of Multiphase Flow in Power Engineering), Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinnian He & Kaitai Li

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  1. Yinnian He
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  2. Kaitai Li
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Correspondence to Yinnian He.

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Mathematics Subject Classification (2000): 35Q10, 65M10, 65N30, 76D05

Revised version received January 26, 2004

Subsidized by the Special Funds for Major State Basic Research Projects G1999032801-07, NSF of China 10371095, NSF of China 10101020 and NSF of China 50323001.

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He, Y., Li, K. Asymptotic behavior and time discretization analysis for the non-stationary Navier-Stokes problem. Numer. Math. 98, 647–673 (2004). https://doi.org/10.1007/s00211-004-0532-y

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  • DOI: https://doi.org/10.1007/s00211-004-0532-y

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