The well-posedness for the Cauchy problem of the double-diffusive convection system

Abstract

In this paper, we consider the well-posedness of the solution for the Cauchy problem of the double-diffusive convection system in R3. We establish the local existence and uniqueness of the solution for the double-diffusive convection system in H1(R3) with large initial data and the global well-posedness under the assumption that the L2 norm of the initial data is small. Moreover, we also prove that there exists a global unique solution in HN(R3) for any N ≥ 2, without any other smallness condition of the initial data.