Analysis of a thin film approximation for two-fluid Taylord-Couette flows
In this work we study the evolution of the interface between two different fluids in two concentric cylinders when the velocity is given by the Navier-Stokes equation and one of the fluids is thin. We present a formal asymptotic derivation of the evolution equation for the interface under different...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
31.05.2019
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this work we study the evolution of the interface between two different
fluids in two concentric cylinders when the velocity is given by the
Navier-Stokes equation and one of the fluids is thin. We present a formal
asymptotic derivation of the evolution equation for the interface under
different scaling assumptions for the surface tension. We then study the
different types of the stationary solutions and travelling waves for the
resulting equation. In particular, we state a global well posedness result and
using Center Manifold Theory, we obtain detailed information about the long
time asymptotics of the solutions of the problem. |
|---|---|
| AbstractList | In this work we study the evolution of the interface between two different
fluids in two concentric cylinders when the velocity is given by the
Navier-Stokes equation and one of the fluids is thin. We present a formal
asymptotic derivation of the evolution equation for the interface under
different scaling assumptions for the surface tension. We then study the
different types of the stationary solutions and travelling waves for the
resulting equation. In particular, we state a global well posedness result and
using Center Manifold Theory, we obtain detailed information about the long
time asymptotics of the solutions of the problem. |
| Author | Pernas-Castaño, Tania Velázquez, Juan J. L |
| Author_xml | – sequence: 1 givenname: Tania surname: Pernas-Castaño fullname: Pernas-Castaño, Tania – sequence: 2 givenname: Juan J. L surname: Velázquez fullname: Velázquez, Juan J. L |
| BackLink | https://doi.org/10.48550/arXiv.1905.13606$$DView paper in arXiv |
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| Snippet | In this work we study the evolution of the interface between two different
fluids in two concentric cylinders when the velocity is given by the
Navier-Stokes... |
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| SubjectTerms | Mathematics - Analysis of PDEs |
| Title | Analysis of a thin film approximation for two-fluid Taylord-Couette flows |
| URI | https://arxiv.org/abs/1905.13606 |
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