Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 320, Issue 2, Pages 395-424Publisher
SPRINGER
DOI: 10.1007/s00220-013-1708-z
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Funding
- NSF [DMS-1211806]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1211806] Funding Source: National Science Foundation
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We investigate regularity and well-posedness for a fluid evolution model in the presence of a three-phase contact point. We consider a fluid evolution governed by Darcy's Law. After linearization, we obtain a nonlocal third order operator which contains the Dirichlet-Neumann operator on the wedge with opening angle . We show well-posedness and regularity for this linear evolution equation. In the limit of vanishing opening angle, we show the convergence of solutions to a fourth order degenerate parabolic operator, related to the thin-film equation. In the course of the analysis, we introduce and characterize a new type of sum of weighted Sobolev spaces which are suitable to capture the singular limit as . In particular, the nature of the problem requires the use of techniques that are adapted to the problem in the singular domain as well as the degenerate limit problem.
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