On Singularity Formation in a Hele-Shaw Model
نویسندگان
چکیده
منابع مشابه
On singularity formation in a Hele-Shaw model
We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in [CDG93] and widely studied since. The model consists of a single one dimensional evolution equation for the thickness 2h = 2h(x, t) of a thin neck of fluid, ∂th+ ∂x(h ∂ 3 xh) = 0 , for x ∈ (−1, 1) and t ≥ 0. The boundary conditions fix the neck height and the pressure jump...
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We provide numerical and analytic evidence for the formation of a singu-larity driven only by surface tension in the mathematical model describing a two-dimensional Hele-Shaw cell with no air injection. Constantin and Pugh have proved that no such singularity is possible if the initial shape is close to a circle; thus we show that their result is not true in general. Our evidence takes the form...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2018
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-018-3241-6