On the well-posedness of a mathematical model describing water-mud interaction

Details On the well-posedness of a mathematical model describing water-mud interaction On the well-posedness of a mathematical model describing water-mud interaction

2012-02-14

arxiv.org/abs/1202.2965v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

In this paper we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared to its depth. The mud is treated as a non-Netwonian fluid and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory.

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