Publication Date:
2011-03-23
Description:
We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (α,f0(α)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time t∗ where the solution of the free boundary problem parameterized as (α,f(α,t)) blows up: ‖∂αf‖L∞(t∗) = ∞. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh–Taylor condition changes sign and the solution breaks down.
Print ISSN:
0027-8424
Electronic ISSN:
1091-6490
Topics:
Biology
,
Medicine
,
Natural Sciences in General
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