Global well-posedness of solutions for the sixth order convective Cahn-Hilliard equation
Received:March 06, 2020  Revised:July 22, 2020
Key Word: Global smooth solution, sixth order convective Cahn-Hilliard equation, Cauchy problem, local existence.
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 Author Name Affiliation E-mail Xiaopeng Zhao Northeastern University zhaoxiaopeng@jiangnan.edu.cn Fengnan Liu Dalian University of Technology Haichao Meng Changzhou Luoyang high school
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In this paper, we consider the small initial data global well-posedness of smooth solutions for the Cauchy problem of sixth order convective Cahn-Hilliard equation. 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 $\bar{u}\in\mathbb{R}$.