Mathematical analysis for local structures of viscous incompressible flows
| Project/Area Number |
22740090
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kobe University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 偏微分方程式 / 流体力学 / 非圧縮性粘性流体 / Navier-Stokes方程式 / 渦度方程式 / 安定性解析 / 解の漸近挙動 / 境界層 / 渦度場 / 非線形偏微分方程式 / 高レイノルズ数 / 粘性零極限 / 基本解の評価 / スケール変換不変性 / 自己相似解 / 線形作用素の半群理論 |
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| Research Abstract |
It is well-known that vorticity fields play important roles in dynamics of incompressible flows. This research aims to analyze linear and nonlinear partial differential equations related with vorticity fields mathematically. The research in particular has made important contributions in the following topics:
(i) Stability analysis of some stationary solutions modeling vortex tubes in turbulent flows;
(ii) Estimates of fundamental solutions to fractional diffusion equations with a drift;
(iii) Analysis of vorticity equations in the half plane and its applications to inviscid limit problem for the Navier-Stokes equations.
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Report
(4 results)
Research Products
(58 results)
