| Budget Amount *help |
¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Outline of Final Research Achievements |
To establish mathematical theory for bifurcation and stability in the compressible Navier-Stokes equation, we studied the stability of stationary and time-periodic parallel flows. We proved that the asymptotic behavior of parallel flow is described by a linear heat equation when the space dimension n is greater than or equal to 3, and by a one-dimensional viscous Burgers equation when n=2. In the case of the Poiseuille flow, we derived a sufficient condition for the instability in terms of the Reynolds and Mach numbers. Furhtermore, we proved the bifurcation of a familiy of space-time-peirodic traveling waves when the Poiseuille flow is getting unstable. As a first step of the stability analysis of space-periodic patterns, we investigate the stablity of the motionless state on periodic infinte layer, and derived the asymptotic leading part of the perturbation by using the Bloch transformation.
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