Periodic solutions of the heat convection equations in exterior domains
Kazuo Ōeda · Proceedings of the Japan Academy Series A Mathematical Sciences · 1997
Q-K 1 where K is a compact set whose boundary K is of class C .W e put and 2-f) (0, co).Then we consider the periodic problem for the heat convection equation (HCE):O, for t> 0,(3) u(', T) u(., 0), 0(', T) 0(', 0).Here u u(x) is the velocity vector, p p(x) is the pressure and 0 0(x) is the temperature; v, :, o, p and g g(x)are the kinematic viscos- ity, the thermal conductivity, the coefficient of volume expansion, the density at 0 O and the gravitational vector, respectively.As for the ex- terior problem of (HCE), Hishida [2] showed the