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, sixth order Cahn-Hilliard equation, uniqueness, oil-water-surfactant mixtures.
AB - <p style="text-align: justify;">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.</p>