The modelling of microconvection in an infinite strip

A model of the microconvection of an isothermally incompressible fluid, which can be used to investigate convection in weak force fields and on microscopic scales and can be characterized by non-solenoidality of the velocity field, is considered. An invariant solution in an infinite vertical strip occupied by a fluid is studied in the case where the heat flux on the two opposite faces of the strip fluctuates in antiphase. The use of the model of microconvection to construct an invariant solution gives rise to several non-standard-value initial-boundary problems. Their solvability in classes of Holder functions is proved.