Skip to main content
SpringerLink
Log in

Normal solutions to boundary value problems for stationary systems of the Navier-Stokes type

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

References

  1. J.-L. Lions, Control of Singular Distributed Systems [Russian translation], Nauka, Moscow (1987).

    Google Scholar 

  2. A. V. Fursikov, “Control problems and theorems related to unique solvability for a mixed boundary value problem of the three-dimensional Navier-Stokes and Euler equations,” Mat. Sb.,115, No. 2, 281–306 (1981).

    Google Scholar 

  3. A. V. Fursikov, “Properties of solutions to some extremal problems related to the Navier-Stokes system,” Mat. Sb.,118, No. 3, 323–349 (1982).

    Google Scholar 

  4. M. D. Gunzburger, L. Hoo, and T. P. Svobodny, “Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls,” Math. Comp.,57, No. 195, 123–151 (1991).

    Google Scholar 

  5. M. D. Gunzburger, L. Hoo, and T. P. Svobodny, “Boundary velocity control of incompressible flow with an application to viscous drag reduction,” SIAM J. Control Optim.,30, No. 1, 167–181 (1992).

    Article  Google Scholar 

  6. A. Yu. Chebotarëv, “Optimal control in the leakage problem for the equation of an ideal fluid,” Dinamika Sploshn. Sredy (Novosibirsk),81, 138–150 (1987).

    Google Scholar 

  7. A. Yu. Chebotarëv, “On unilateral and extremal problems related to the Stokes system,” Dinamika Sploshn. Sredy (Novosibirsk),102, 133–147 (1991).

    Google Scholar 

  8. A. Yu. Chebotarëv, “Subdifferential boundary value problems for the stationary Navier-Stokes equations,” Differentsial'nye Uravneniya,28, No. 8, 1443–1450 (1992).

    Google Scholar 

  9. A. Yu. Chebotarëv, “Extremal boundary value problems of the dynamics of a viscous incompressible fluid,” Sibirsk. Mat. Zh.,34, No. 5, 202–213 (1993).

    Google Scholar 

  10. A. Yu. Chebotarëv, “Maximum principle in the boundary control problem for flow of a viscous fluid,” Sibirsk. Mat. Zh.,34, No. 6, 189–197 (1993).

    Google Scholar 

  11. S. S. Sritharan, “Dynamic programming of the Navier-Stokes equations,” Systems Control Lett.,16, 299–307 (1991).

    Article  Google Scholar 

  12. S. S. Sritharan, “Pontryagin maximum principle and dynamic programming for viscous hydrodynamics,” in: Optimization and Nonlinear Analysis, 1992, pp. 286–297 (Pitman Research Notes in Math.,244).

    Google Scholar 

  13. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  14. E. B. Bykhovskii and N. V. Smirnov, “Orthogonal decompositions of the space of vector-functions square-summable on a given domain,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR, No. 59, 6–36 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vladivostok

    A. Yu. Chebotarëv

Authors
  1. A. Yu. Chebotarëv
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research was partially supported by the “Russian Universities” program within the section “Fundamental Problems of Mathematics and Mechanics” (Grant 1.5.53).

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 934–942, July–August, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chebotarëv, A.Y. Normal solutions to boundary value problems for stationary systems of the Navier-Stokes type. Sib Math J 36, 807–815 (1995). https://doi.org/10.1007/BF02107339

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02107339

Keywords

Search

Navigation