On the Rayleigh-Plateau instability. The regularity in \(H^{3}_{\mathrm{per}}\) (Q2823230)
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scientific article; zbMATH DE number 6634039
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Rayleigh-Plateau instability. The regularity in \(H^{3}_{\mathrm{per}}\) |
scientific article; zbMATH DE number 6634039 |
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6 October 2016
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Rayleigh-Plateau instability
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nonlinear parabolic PDE
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thin films
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On the Rayleigh-Plateau instability. The regularity in \(H^{3}_{\mathrm{per}}\) (English)
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This paper discusses the Rayleigh-Plateau instability of a cylindrical pore that is mathematically modelled by the fourth order parabolic equation NEWLINE\[NEWLINE \frac{\partial h}{\partial t}=-\frac{1}{h}\frac{\partial}{\partial x}\left( h\frac{\partial^3 h}{\partial x^3}\right)\quad \text{ on }(0,T)\times (0,1), NEWLINE\]NEWLINE where \(h(1,\cdot)\) is periodic on \((0,1)\), \(h(0,\cdot)=h_0>0\) is a periodic function on \((0,1)\).NEWLINENEWLINELocal and global existence of solution, as well as convergence to the mean value of the initial data are obtained.
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