| 六阶对流Cahn-Hilliard方程解的整体适定性 |
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| 引用本文： | 赵晓朋,刘凤楠,孟海潮.六阶对流Cahn-Hilliard方程解的整体适定性[J].数学研究及应用,2021,41(2):150-160. |
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| 作者姓名： | 赵晓朋 刘凤楠 孟海潮 |
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| 作者单位： | 东北大学理学院, 辽宁 沈阳 110819;大连理工大学数学科学学院, 辽宁 大连 116024;江南大学理学院, 江苏 无锡 214122 |
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| 基金项目： | 中央高校基本科研业务费(Grant No.N2005031). |
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| 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 L1 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■.
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| 关 键 词： | Global smooth solution sixth order convective Cahn-Hilliard equation Cauchy problem local existence |
| 收稿时间： | 2020/3/6 0:00:00 |
| 修稿时间： | 2020/9/7 0:00:00 |
Global Well-Posedness of Solutions for the Sixth Order Convective Cahn-Hilliard Equation |
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| Xiaopeng ZHAO,Fengnan LIU,Haichao MENG.Global Well-Posedness of Solutions for the Sixth Order Convective Cahn-Hilliard Equation[J].Journal of Mathematical Research with Applications,2021,41(2):150-160. |
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| Authors: | Xiaopeng ZHAO Fengnan LIU Haichao MENG |
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| Institution: | College of Sciences, Northeastern University, Liaoning 110819, P. R. China;School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China; School of Science, Jiangnan University, Jiangsu 214122, P. R. China |
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| Abstract: | 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 $\bar{u}\in\mathbb{R}$. |
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| Keywords: | Global smooth solution sixth order convective Cahn-Hilliard equation Cauchy problem local existence |
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