Global nonlinear stability in the Benard problem for a mixture near the bifurcation point

The nonlinear stability of the motionless state of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme, for stress-free and rigid-rigid boundary conditions and Schmidt numbers PC greater than Prandtl numbers PT, is studied in the region around the bifurcation point C-0(2) = R-B(2) (PT + 1) / [P-T (p - 1)] of linear instability. An improvement of the results in Mulone [11] is found for small values of p = P-C / P-T and P-T. For p sufficiently large the critical nonlinear Rayleigh number is very close to the linear one (with relative difference less than 1% in the sea water case).