Existence and uniqueness theorems for a steady thermo-diffusive mixture in a mixed problem

摘要: It is known ([l-3]) that, in a chemical homogeneous fluid, small changes of density, induced by temperature gradients, will induce convection currents. The most important case certainly the BCnard problem fluid layer heated from below (see [l, 31 and references therein). In binary mixture there can be convective motions due to density variations concentration gradients [l-3]). study for mixtures great importance many applications such as oceanology, metereology, astrophysics, geophysics, etc. This has been studied within scheme Oberbeck-Boussinesq equations (OB) several authors [l-151$. Nevertheless, only few take into account interactions between thermal diffusion thermal-diffusive conduction, [2,4-6,11,14]. worth noting physical point view, one should aforesaid every which not “too small”. Up this date, far we know, wellposedness problem, mixed boundary conditions, yet proved. aim present paper prove existence uniqueness theorems steady solution OB with when thermo-diffusive are neglected. region motion 9 c R3 assumed bounded smooth part rigid “free but invariable” (i.e. system coordinates chosen it does change). On give usual adherence conditions velocity field assign fields. free slip (which correspond normal component tangential stress vector) heat mass fluxes. value represents first steps towards more general problems domain boundary. kind studied-for an isothermal fluid-by e.g. [3,16-201 [IS]).