Some complex equations arising in hele shaw flow
نویسندگان
چکیده
منابع مشابه
Some Numerical Methods for the Hele-Shaw Equations
In ([19, 20]), Tryggvason and Aref use a boundary integral method and the vortex-in-cell method to evolve the interface between two fluids in a Hele-Shaw cell. The method gives excellent results for intermediate values of the nondimensional surface tension parameter. The results are different from the predicted results of McLean and Saffman for small surface tension. For large surface tension, ...
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We study the Saffman-Taylor instability of a non-Newtonian fluid in a Hele-Shaw cell. Using a fluid model with shear-rate dependent viscosity, we derive a Darcy’s law whose viscosity depends upon the squared pressure gradient. This yields a natural, nonlinear boundary value problem for the pressure. A model proposed recently by Bonn et al. @Phys. Rev. Lett. 75, 2132 ~1995!# follows from this mo...
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This thesis discusses the radial version of the Hele-Shaw problem. Different from the channel version, traveling-wave solutions do not exist in this version. Under algebraic potentials, in the case that the droplets expand, in finite time, cusps will appear on the boundary and classical solutions may not exist afterwards. Physicists have suggested that for (2p+ 1, 2)-cusps, that near cusp singu...
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The one-phase Hele-Shaw flow has a long history and has been extensively studied from several point of views ranging from the fluid dynamical beginnings to complex analysis and integrable systems, see [5]. We prove existence, using the implicit function theorem, of a solution Wε in the Bochner space L2(0, T ;H1 0 (Ω;Rm)) to a non-local in time semi-linear system of coupled PDEs of second order ...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1993
ISSN: 0893-9659
DOI: 10.1016/0893-9659(93)90098-8