Skip to main content
Log in

On the Stokes problem with nonzero divergence

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

The strong solvability of the nonstationary Stokes problem with nonzero divergence in a bounded domain is studied. Bibliography: 12 titles.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. V. Besov, V. P. Il’in, and S. M. Nikolskii, Integral Representations of Functions and Imbedding Theorems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  2. M. E. Bogovskii, “On solution of some problems of vectoral analysis related to div and grad operators,” in: Proceedings of the S. L. Sobolev Seminar, 1 (1980), pp. 5-40.

    MathSciNet  Google Scholar 

  3. L. Caffarelli, R. V. Kohn, and L. Nirenberg, “Partial regularity of suitable weak solutions of the Navier-Stokes equations,” Comm. Pure Appl. Math., 35, 771-831 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Farwig and H. Sohr, “The stationary and nonstationary Stokes system in exterior doamains with nonzero divergence and nonzero boundery data,” Math. Meth. Appl. Sci., 17, 269-291 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  5. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, Rhode Island (1967).

    MATH  Google Scholar 

  6. G. A. Seregin, “Some estimates near the boundary for solutions to the nonstationary linearized Navier-Stokes equations,” Zap. Nauchn. Semin. POMI, 271, 204-223 (2000).

    Google Scholar 

  7. G. A. Seregin, “Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary,” J. Math. Fluid Mech., 4, no. 1, 1-29 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. G. A. Seregin, “Local regularity theory of the Navier-Stokes equations,” in: Handbook of Mathematical Fluid Dynamics, Vol. 4 (2007), pp. 159-200.

  9. V. A. Solonnikov, “Estimates in L p of solutions to the initial-boundary value problem for the generalized Stokes system in a bounded domain,” Probl. Math. Anal., 21, 211-263 (2000).

    MATH  Google Scholar 

  10. V. A. Solonnikov, “Estimates of solutions of the Stokes equations in Sobolev spaces with a mixed norm,” Zap. Nauchn. Semin POMI, 288, 204-231 (2002).

    Google Scholar 

  11. V. A. Solonnikov, “On the estimates of solutions of nonstationary Stokes problem in anisotropic Sobolev spaces and on the estimate of resolvent of the Stokes problem,” Usp. Mat. Nauk, 58, no. 2 (350), 123-156 (2003).

    Google Scholar 

  12. D. K. Faddeev, B. Z. Vulich, V. A. Solonnikov, and N. N. Uraltseva, Selected Chapters in Analysis and Higher Algebra [in Russian], LGU (1981).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Filinov.

Additional information

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 370, 2009, pp. 184–202.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Filinov, N., Shilkin, T. On the Stokes problem with nonzero divergence. J Math Sci 166, 106–117 (2010). https://doi.org/10.1007/s10958-010-9849-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-010-9849-5

Keywords

Navigation