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

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.

___

  • 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.