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| Content Provider | Springer Nature Link |
|---|---|
| Author | Escher, Joachim Matioc, Bogdan Vasile Ehrnström, Mats |
| Copyright Year | 2010 |
| Abstract | We study the radial movement of an incompressible fluid located in a Hele–Shaw cell rotating at a constant angular velocity in the horizontal plane. Within an analytic framework, local existence and uniqueness of solutions is proved, and it is shown that the unique rotationally invariant equilibrium of the flow is unstable. There are, however, other time-independent solutions: using surface tension as a bifurcation parameter we establish the existence of global bifurcation branches consisting of stationary fingering patterns. The same results can be obtained by fixing the surface tension while varying the angular velocity. Finally, it is shown that the equilibria on a global bifurcation branch converge to a circle as the surface tension tends to infinity, provided they stay suitably bounded. |
| Ending Page | 293 |
| Page Count | 23 |
| Starting Page | 271 |
| File Format | |
| ISSN | 14226928 |
| e-ISSN | 14226952 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Issue Number | 2 |
| Volume Number | 13 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2010-02-04 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Fourier coefficients, Fourier series of functions with special properties, special Fourier series Mathematical Methods in Physics Fingering patterns Hele–Shaw cell Fluid- and Aerodynamics PDEs in connection with fluid mechanics Bifurcation Abstract parabolic equations Bifurcations and instability Equilibria Well-posedness Classical Continuum Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics |
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