Analysis of a Cahn-Hilliard-Ladyzhenskaya system with singular potential

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:397

Article

Bosia, Stefano^1,2 

[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[2] Ecole Polytech, Mecan Solides Lab, F-91128 Palaiseau, France

关键词: Incompressible viscous fluids;    Non-Newtonian fluids;    Ladyzhenskaya model;    Binary mixtures;    Diffuse interfaces;    Cahn-Hilliard equations;    Singular potential;    Trajectory attractors;   

DOI  :  10.1016/j.jmaa.2012.07.053

来源: Elsevier

【 摘 要 】

The evolution of a mixture of two incompressible and (partially) immiscible fluids is here described by Ladyzhenskaya-Navier-Stokes type equations for the (average) fluid velocity coupled with a convective Cahn-Hilliard equation with a singular (e.g., logarithmic) potential. The former is endowed with no-slip boundary conditions, while the latter is subject to no-flux boundary conditions so that the total mass is conserved. Here we first prove the existence of a weak solution in three-dimensions and some regularity properties. Then we establish the existence of a weak trajectory attractor for a sufficiently general time-dependent external force. Finally, taking advantage of the validity of the energy identity, we show that the trajectory attractor actually attracts with respect to the strong topology. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free