Global well-posedness for the 2D fluid system with the linear Soret effect and Yudovich's type data

In this paper, we are concerned with the Cauchy problem of the two-dimensional (2D) fluid system with the linear Soret effect and Yudovich's type data. We obtain global unique solution for this system without imposing any smallness conditions on the initial data. Our methods mainly rely upon Littlewood-Paley theory and loss of regularity estimates.