Global gevrey regularity for the Benard convection in a porous medium with zero Darcy-Prandtl number uri icon

abstract

  • In this paper, we prove the existence and uniqueness for the three-dimensional Bnard convection model in a porous medium with zero Darcy-Prandtl number using the Galerkin procedure. In addition, we show that the solutions to this problem are analytic in time with values in a Gevrey class regularity. We also prove that the solution of the standard Galerkin method converges exponentially fast, in the wave number, to the exact solution. This gives an analytical justification to the two-dimensional computational results of Graham, Steen, and Titi [J. Nonlin. Sci. 3 (1993), 153-167].

published proceedings

  • JOURNAL OF NONLINEAR SCIENCE

author list (cited authors)

  • Ly, H. V., & Titi, E. S.

citation count

  • 26

complete list of authors

  • Ly, HV||Titi, ES

publication date

  • June 1999