Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation

Abstract

This paper is concerned with the local well-posedness of the Oberbeck Boussinesq approximation for the unsteady motion of a drop in another fluid separated by a closed interface with surface tension. We are devoted to obtaining the linearized Oberbeck-Boussinesq approximation in the fixed domain by using the Hanzawa transformation, and using maximal $ L^{p} $-$ L^{q} $ regularities for the two-phase fluid motion of the linearized system obtained by the authors in [10] to establish the existence and uniqueness of the solutions of nonlinear problem with the help of the contraction mapping principle, in which the differences of nonlinear terms are estimated.