Skip to main content
SpringerLink
Log in

On the rotating Navier-Stokes equations with mixed boundary conditions

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li, K. T., Su, J., Gao, L. M.: Optimal Shape Design for Blade’s Surface of an Impeller via the Navier-Stokes Equations. Communications in Numerical Methods in Engineering, 22(4), 657–676 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Li, K. T., Su, J., Huang, A. X.: Geometry design of blade’s surface and boundary control of Navier-Stokes equations. Academic Journal of Xi’an Jiaotong University, 19(1), 1–6 (2007)

    MATH  Google Scholar 

  3. Kucera, P., Skalak, Z.: Local Solutions to the Navier-Stokes Equations with Mixed Boundary Conditions. Acta Application Mathematics, 54(3), 275–288 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kracmar, S., Neustupa, J.: A weak solvability of a steady variational inequality of the Navier-Stokes type with mixed boundary conditions. Nonlinear Analysis, 47, 4169–4180 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Heywood, J. G., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids, 22, 325–352 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Temam, R.: Navier-Stokes Equations and Nonlinear Functional Analysis, SIAM, Philadelphia, 1983

    Google Scholar 

  7. Constaintin, P., Foias, C.: Navier-Stokes Equations, University of Chicago Press, Chicago, 1988

    Google Scholar 

  8. Heywood, J. G.: The Navier-Stokes Equations: On the existence, regularity and decay of solutions. Indiana University Mathematics Journal, 29(5), 639–681 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fujita, H.: On the existence and regularity of the steady state solutions of the Navier-Stokes equation. J. Fac. Sci. Univ. Tokyo Sect. I A Math., 9, 59–102 (1961)

    Google Scholar 

  10. Glowinski, R.: Finite Element Methods for Incompressible Viscous Flow, Handbook of Numerical Analysis, IX, 2003

  11. Kloucek, P., Rys, F. S.: On the stability of the fractional step-ϑ-scheme for the Navier-Stokes equations. SIAM J. Numer. Anal., 31, 1312–1335 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Burgers, J.: A mathematical model illustrating the theory of turbulence, Advances in Applied Mechanics, Academic Press, New York, 1948

    Google Scholar 

  13. Burgers, J.: The nonlinear diffusion equation, D. Reidel, Dordrecht, 1974

    MATH  Google Scholar 

  14. Hayashi, N., Naumkin, Pavel I.: Asymptotics for the Korteweg-de Vries-Burgers equation. Acta Mathematica Sinica, English Series, 22(5), 1441–1456 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Yuan, B. Q.: The Cauchy problems and global solutions to the Deybe system and Burgers’ equations in Pseudomeasure spaces. Acta Mathematica Sinica, English Series, 23(3), 439–448 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Xi’an Jiaotong University, Xi’an, 710049, P. R. China

    Kai Tai Li & Rong An

Authors
  1. Kai Tai Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rong An
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kai Tai Li.

Additional information

Supported by the National Nature Science Foundation of China (Grants No. 50306019, No. 10571142, No. 10471110 and No. 10471109)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, K.T., An, R. On the rotating Navier-Stokes equations with mixed boundary conditions. Acta. Math. Sin.-English Ser. 24, 577–598 (2008). https://doi.org/10.1007/s10114-007-1032-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-007-1032-7

Keywords

k]MR(2000) Subject Classification

Search

Navigation