Global well-posedness of mild solution to the 3D Boussinesq system with damping

Abstract

In [27], we pointed out, it seems one can not obtain a global well-posedness of mild solution to the Boussinesq system in Lei-Lin space χ−1. In this paper, to understand this fact well, we consider the well-posedness problem of the Boussinesq system with velocity or thermal damping. Compared with the Boussinesq system, one can show that the mild solution of the Boussinesq system with damping exists globally in Lei-Lin space. Furthermore, by a similar argument, we found it possible to obtain the global well-posedness of mild solution to an Oldroyd-B type model as some parameters are sufficiently small.