Global solvability for double-diffusive convection system based on Brinkman--Forchheimer equation in general domains

Abstract

Abstract In this paper, we are concerned with the solvability of the in itial boundary value problem of a system which describes double-diffusive conve ction phenomena in some porous medium under general domains, especially unbounded domains. In previous works where the boundedness of the space domain is imposed, s ome global solvability results have been already derived. However, when we cons ider our problem in general domains, some compactness theorems are not availab le. Hence it becomes difficult to follow the same strategies as before. Neverthel ess, we can assure the global existence of a unique solution via the contraction me thod. Moreover, it is revealed that the global solvability holds for higher space di mension and larger class of the initial data than those assumed in previous works.