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

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• 作者：Yinnian He^a ; ^{heyn@mail.xjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xinlong Feng^b ; ^{fxlmath@xju.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Navier&ndash ; Stokes/Cahn&ndash ; Hilliard phase field model ; Mixed weak formulation ; Sharp a priori estimates ; H2H2-regularity ; Time derivative of the solution
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：441
• 期：2
• 页码：815-829
• 全文大小：383 K

文摘

In this paper, we provide the uniform H²$H^2$-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,∞)$t\in (0,\infty )$. Based on sharp a priori estimates for the solution of model under weak assumptions on the initial values, we show that the H²$H^2$-regularity of the solution and its time derivative depends on ε⁻¹${\epsilon }^{-1}$ but is independent of time t.