| 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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| 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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