In this talk, we consider the well-posedness and large time behavior of the Navier-Stokes-Cahn-Hilliard equations. First, for the Cauchy problem of incompressible Navier-Stokes-Cahn-Hilliard equation, we show the local well-posedness, global well-posedness and decay of strong solutions. Moreover, for the initial-boundary value problem of density-dependent incompressible Navier-Stokes-Cahn-Hilliard equation, we study the local well-posedness of strong solutions when the initial density function enjoys a positive lower bound.

 

海报