Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures

Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures

Year:    2020

Author:    Haichao Meng, Xiaopeng Zhao

Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v33.n3.1

Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 3 : pp. 193–207

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

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

Author Details

Haichao Meng

Xiaopeng Zhao

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