The well‐posedness of the double‐diffusive convection system in a bounded domain

Abstract

In this paper, we consider the well‐posedness of the initial and boundary value problem for the double‐diffusive convection system in a bounded domain normalΩ.25em⊂.25emR3. We first prove the local existence of the unique strong solution with large initial data in H01false(normalΩfalse) and then extend it to a global one provided the L2 norm of the initial data is small.