Abstract

We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. for initial data in Hs, s>d2+1, the existence and uniqueness of solution in C([0,T];Hs) ∪L2(0,T;Hs+2) that is global in time in the two-dimensional case (d=2) and local in time in the three-dimensional case (d=3) are established. Several blow-up criterions in the three-dimensional case are provided as well. One of the tools that we utilized is the Littlewood-Paley theory in order to establish certain key commutator estimates. © 2012 Elsevier Masson SAS.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant 1008852

Keywords and Phrases

Blow-Up Criterion; Hele-Shaw-Cahn-Hilliard; Well-Posedness

International Standard Serial Number (ISSN)

0294-1449

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2023 EMS Press, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jan 2013

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