On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness
Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in...
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| Veröffentlicht in: | Journal of nonlinear science 2024-06, Vol.34 (3), Article 43 |
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| creator | Peter, Malte A. Woukeng, Jean Louis |
| description | Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn–Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously. |
| doi_str_mv | 10.1007/s00332-024-10018-6 |
| format | Article |
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| subjects | Analysis Classical Mechanics Economic Theory/Quantitative Economics/Mathematical Methods Homogenization Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical Two phase flow Well posed problems |
| title | On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness |
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