Uniform H2-regularity of solution for the 2D Navier–Stokes/Cahn–Hilliard phase field model

In this paper, we provide the uniform H2H2-regularity results with respect to small perturbation parameter ε   of the solution and its time derivative for the 2D Navier–Stokes/Cahn–Hilliard phase field model with t∈(0,∞)t∈(0,∞). Based on sharp a priori estimates for the solution of model under weak assumptions on the initial values, we show that the H2H2-regularity of the solution and its time derivative depends on ε−1ε−1 but is independent of time t.