Volume 33, Issue 3
Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures

J. Part. Diff. Eq., 33 (2020), pp. 193-207.

Published online: 2020-06

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• Abstract

In this paper, by using the $L_p$-$L_q$-estimates, regularization property of the linear part of $e^{-t\Delta^3}$ and successive approximations, we consider the existence and uniqueness of global   mild solutions to the   sixth-order Cahn-Hilliard equation arising in oil-water-surfactant mixtures in suitable spaces, namely $C^0([0,T];\dot{W}^{2,\frac{N(l-1)}2}(\Omega))$ when the norm $\|u_0\|_{\dot{W}^{2,\frac{N(l-1)}2}(\Omega)}$ is sufficiently small.

• Keywords

Global solution sixth order Cahn-Hilliard equation uniqueness oil-water-surfactant mixtures.

35K55, 35A01, 35B45

mhaichao@126.com (Haichao Meng)

zhaoxiaopeng@mail.neu.edu.cn (Xiaopeng Zhao)

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@Article{JPDE-33-193, author = {Meng , Haichao and Zhao , Xiaopeng}, title = {Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {3}, pages = {193--207}, abstract = {

In this paper, by using the $L_p$-$L_q$-estimates, regularization property of the linear part of $e^{-t\Delta^3}$ and successive approximations, we consider the existence and uniqueness of global   mild solutions to the   sixth-order Cahn-Hilliard equation arising in oil-water-surfactant mixtures in suitable spaces, namely $C^0([0,T];\dot{W}^{2,\frac{N(l-1)}2}(\Omega))$ when the norm $\|u_0\|_{\dot{W}^{2,\frac{N(l-1)}2}(\Omega)}$ is sufficiently small.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/17069.html} }
TY - JOUR T1 - Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures AU - Meng , Haichao AU - Zhao , Xiaopeng JO - Journal of Partial Differential Equations VL - 3 SP - 193 EP - 207 PY - 2020 DA - 2020/06 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/17069.html KW - Global solution KW - sixth order Cahn-Hilliard equation KW - uniqueness KW - oil-water-surfactant mixtures. AB -

In this paper, by using the $L_p$-$L_q$-estimates, regularization property of the linear part of $e^{-t\Delta^3}$ and successive approximations, we consider the existence and uniqueness of global   mild solutions to the   sixth-order Cahn-Hilliard equation arising in oil-water-surfactant mixtures in suitable spaces, namely $C^0([0,T];\dot{W}^{2,\frac{N(l-1)}2}(\Omega))$ when the norm $\|u_0\|_{\dot{W}^{2,\frac{N(l-1)}2}(\Omega)}$ is sufficiently small.

Haichao Meng & Xiaopeng Zhao. (2020). Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures. Journal of Partial Differential Equations. 33 (3). 193-207. doi:10.4208/jpde.v33.n3.1
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