On heat convection equations in a half space with non-decaying data and Stokes semi-group on Besov spaces based on [formula omitted

Abstract

The local existence theorem for the Boussinesq equations in the half space R + n + 1 = { x = ( x ˜ , x n ) ∈ R n + 1 ; x ˜ ∈ R n , x n + 1 > 0 } with non-decaying data is shown. To this end, the Stokes operator is shown to generate an analytic semi-group on the Besov spaces of negative order based on L ∞ .