The higher-order convective Cahn-Hilliard equation describes the evolution of crystal surfaces faceting through surface electromigration, the growing surface faceting, and the evolution of dynamics of phase transitions in ternary oil-water-surfactant systems. In this paper, we study the $H^3$ solutions of the Cauchy problem and prove, under different assumptions on the constants appearing in the equation and on the mean of the initial datum, that they are well-posed.

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关于高阶对流Cahn-Hilliard型方程解的一个注记

高阶对流Cahn-Hilliard方程描述了通过表面电迁移的晶体表面刻面的演化，生长的表面刻面以及三元油-水-表面活性剂系统中相变动力学的演化。在本文中，我们研究了$H^3$ 柯西问题的解，并在不同的假设下，根据方程式中出现的常数和初始基准的均值，证明它们是正确的。