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 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Setsunan University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2016-03-31
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Project Status |
Completed (Fiscal Year 2015)
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Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | ナヴィエ・ストークス方程式 / 自由表面問題 / 液膜流 / 長波長近似 / 自由表面流 / Navier-Stokes方程式 / Benney-Gjevik方程式 / 自由境界問題 / Kornの不等式 / Poincareの不等式 |
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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Report
(5 results)
Research Products
(15 results)