Research Article
BibTex RIS Cite
Year 2019, Volume: 68 Issue: 1, 87 - 97, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443638

Abstract

References

  • Ahn, C.T., Quyet, D.T. and Tinh, D.T., Existence and finite time approximation of strong solutions to the 2D g-Navier-Stokes equations. Acta Math. Vietnam. 38 (2013) 413-428.
  • Brezis, H. and Gallouet, T., Nonlinear Schrodinger evolution equations. Nonlinear Analysis, Theory, Methods & Applications, (1980) 677--681.
  • Cao, Y. and Titi, E.S.,On the rate of convergence of the two-dimensional α-models of turbulence to the Navier-Stokes Equations. Numer. Funct. Anal. Optim. 30. (2009) 11-12:1231--1271.
  • Constantin, P. and Foias C., Navier-Stokes equations. University of Chicago Press, Chicago, (1988).
  • Foias, C. , Manley, O., Rosa, R. and Temam R., Navier-Stokes equations and turbulence. Encyclopedia of Mathematics and its Applications, 83. Cambridge University Press, Cambridge, (2001).
  • Courant, R. and Hilbert, D., (1989). Methods of Mathematical Physics Vol. II. John Wiley & Sons, New York.
  • Kwak, M., Kwean, H. and Roh, J., The dimension of attractor of the 2D g-Navier-Stokes equations. J. Math. Anal. Appl. 315. 2 (2006) 436--461.
  • Roh, J., g-Navier Stokes equations. Thesis, University of Minnesota (2001).
  • Roh, J., Convergence of the g-Navier Stokes equations. Taiwanese J. Math. 13. 1 (2009) 189--210.
  • Roh, J., Dynamics of the g-Navier Stokes equations. J. Differential Equations 211. 2 (2005) 452--484.
  • Temam, R., Navier-Stokes equations. Theory and numerical analysis. North-Holland Publishing Co. Amsterdam (1977).
  • Temam, R., Navier-Stokes equations and nonlinear functional analysis. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1983).
  • Titi, E.S. On approximate inertial manifolds to the Navier-Stokes equations. J. Math. Anal. App. 149 (1990) 540--557.

On the rate of convergence of the g-Navier-Stokes equations

Year 2019, Volume: 68 Issue: 1, 87 - 97, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443638

Abstract

In this paper we consider 2D g-Navier-Stokes equations in a bounded domain by Ω. We give an error estimate between the solutions of Galerkin approximation of the g-Navier-Stokes equations and the exact solutions of them.

References

  • Ahn, C.T., Quyet, D.T. and Tinh, D.T., Existence and finite time approximation of strong solutions to the 2D g-Navier-Stokes equations. Acta Math. Vietnam. 38 (2013) 413-428.
  • Brezis, H. and Gallouet, T., Nonlinear Schrodinger evolution equations. Nonlinear Analysis, Theory, Methods & Applications, (1980) 677--681.
  • Cao, Y. and Titi, E.S.,On the rate of convergence of the two-dimensional α-models of turbulence to the Navier-Stokes Equations. Numer. Funct. Anal. Optim. 30. (2009) 11-12:1231--1271.
  • Constantin, P. and Foias C., Navier-Stokes equations. University of Chicago Press, Chicago, (1988).
  • Foias, C. , Manley, O., Rosa, R. and Temam R., Navier-Stokes equations and turbulence. Encyclopedia of Mathematics and its Applications, 83. Cambridge University Press, Cambridge, (2001).
  • Courant, R. and Hilbert, D., (1989). Methods of Mathematical Physics Vol. II. John Wiley & Sons, New York.
  • Kwak, M., Kwean, H. and Roh, J., The dimension of attractor of the 2D g-Navier-Stokes equations. J. Math. Anal. Appl. 315. 2 (2006) 436--461.
  • Roh, J., g-Navier Stokes equations. Thesis, University of Minnesota (2001).
  • Roh, J., Convergence of the g-Navier Stokes equations. Taiwanese J. Math. 13. 1 (2009) 189--210.
  • Roh, J., Dynamics of the g-Navier Stokes equations. J. Differential Equations 211. 2 (2005) 452--484.
  • Temam, R., Navier-Stokes equations. Theory and numerical analysis. North-Holland Publishing Co. Amsterdam (1977).
  • Temam, R., Navier-Stokes equations and nonlinear functional analysis. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1983).
  • Titi, E.S. On approximate inertial manifolds to the Navier-Stokes equations. J. Math. Anal. App. 149 (1990) 540--557.
There are 13 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Meryem Kaya 0000-0002-5932-9105

Özge Kazar 0000-0003-4876-3077

Ülkü Dinlemez Kantar 0000-0002-5656-3924

Publication Date February 1, 2019
Submission Date September 3, 2017
Acceptance Date November 25, 2017
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Kaya, M., Kazar, Ö., & Dinlemez Kantar, Ü. (2019). On the rate of convergence of the g-Navier-Stokes equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 87-97. https://doi.org/10.31801/cfsuasmas.443638
AMA Kaya M, Kazar Ö, Dinlemez Kantar Ü. On the rate of convergence of the g-Navier-Stokes equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):87-97. doi:10.31801/cfsuasmas.443638
Chicago Kaya, Meryem, Özge Kazar, and Ülkü Dinlemez Kantar. “On the Rate of Convergence of the G-Navier-Stokes Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 87-97. https://doi.org/10.31801/cfsuasmas.443638.
EndNote Kaya M, Kazar Ö, Dinlemez Kantar Ü (February 1, 2019) On the rate of convergence of the g-Navier-Stokes equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 87–97.
IEEE M. Kaya, Ö. Kazar, and Ü. Dinlemez Kantar, “On the rate of convergence of the g-Navier-Stokes equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 87–97, 2019, doi: 10.31801/cfsuasmas.443638.
ISNAD Kaya, Meryem et al. “On the Rate of Convergence of the G-Navier-Stokes Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 87-97. https://doi.org/10.31801/cfsuasmas.443638.
JAMA Kaya M, Kazar Ö, Dinlemez Kantar Ü. On the rate of convergence of the g-Navier-Stokes equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:87–97.
MLA Kaya, Meryem et al. “On the Rate of Convergence of the G-Navier-Stokes Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 87-97, doi:10.31801/cfsuasmas.443638.
Vancouver Kaya M, Kazar Ö, Dinlemez Kantar Ü. On the rate of convergence of the g-Navier-Stokes equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):87-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.