2015 Fiscal Year Final Research Report
Mathematical consideration of the long-wave approximation of the liquid thin film flows
| Project/Area Number |
24740060
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Setsunan University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | ナヴィエ・ストークス方程式 / 自由表面問題 |
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| Outline of Final Research Achievements |
We consider the motion of a viscous incompressible fluid flowing down an inclined plane under the effect of gravity. The fluid motion is governed by the Navier-Stokes equations with the free boundary conditions. When the Reynolds number and the angle are sufficiently small, the mathematical justification of the long-wave approximation is known. To obtain a specific range of this ``sufficiently small Reynolds number'’, we examine the spectra of the compact operator arising the linearized problem. Then we calculate about a range of the Reynolds number, when the linear operator has a non-zero eigenvalue.
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| Free Research Field |
数学解析
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