We continue to study an initial boundary value problems to a model describing the evolution in time of diffusive phase interfaces in sea-ice growth. In a previous paper global existence and the long-time of behavior of weak solutions in one space was studied under Dirichlet boundary conditions. Here we show that the global existence of weak solutions and the long-time behavior are also studied under Neumann boundary condition. In this paper we study in space dimension lower than or equal to $3$.