六阶对流Cahn-Hilliard方程解的整体适定性

Global Well-Posedness of Solutions for the Sixth Order Convective Cahn-Hilliard Equation

中文关键词:  整体光滑解  六阶对流Cahn-Hilliard方程  Cauchy问题  局部存在性

英文关键词:Global smooth solution  sixth order convective Cahn-Hilliard equation  Cauchy problem  local existence

中文摘要:

      本文考虑了一个具小初值的六阶对流Cahn-Hilliard方程Cauchy问题光滑解的整体适定性问题. 我们首先构造了一类光滑局部解, 进一步假设初值的$L^1$模充分小且光滑非线性函数$f(u)$和$g(u)$在点$\bar{u}\in\mathbb{R}$处满足局部增长条件, 结合先验估计, 连续性准则, 我们将该局部光滑解延拓到$t>0$.

英文摘要:

      In this paper, we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data. We first construct a local smooth solution, then by combining some a priori estimates, continuity argument, the local smooth solution is extended step by step to all $t>0$ provided that the $L^1$ norm of initial data is suitably small and the smooth nonlinear functions $f(u)$ and $g(u)$ satisfy certain local growth conditions at some fixed point $\bar{u}\in\mathbb{R}$.