Long-Time Behavior for the Hele-Shaw-Cahn-Hilliard System
We study the Hele-Shaw-Cahn-Hilliard system that models two phase incompressible Darcian flow in porous media with matched density but arbitrary viscosity contrast. in the 3D case, we prove eventual regularity of weak solutions, as well as existence of global classical solutions if either the Péclet number is sufficiently small or the initial datum is close to one local energy minimizer of the free energy. in both 2D and 3D, we demonstrate that the ω-limit set of each trajectory consists of a single steady state. Finally, stability of local minimizers is established. © 2012 - IOS Press and the authors. All rights reserved.
X. Wang and H. Wu, "Long-Time Behavior for the Hele-Shaw-Cahn-Hilliard System," Asymptotic Analysis, vol. 78, no. 4, pp. 217 - 245, IOS Press, Aug 2012.
The definitive version is available at https://doi.org/10.3233/ASY-2012-1092
Mathematics and Statistics
Keywords and Phrases
Convergence to Equilibrium; Eventual Regularity; Hele-Shaw-Cahn-Hilliard System; Stability
International Standard Serial Number (ISSN)
Article - Journal
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06 Aug 2012