The well-posedness for the compressible viscous fluid equations for the mathematical analysis of blood flow
| Project/Area Number |
17K14225
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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 |
Mathematical analysis
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| Research Institution | Kanagawa University |
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Principal Investigator |
Murata Miho 神奈川大学, 工学部, 助教 (90754888)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 圧縮性粘性流体 / 圧縮性Navier-Stokes方程式 / Navier-Stokes-Korteweg / 時間局所解 / 時間大域解 / 最大正則性 / 流体数学 / 流体と剛体の連成問題 / 非線形偏微分方程式 |
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| Outline of Final Research Achievements |
In order to analysis the system of equations describing the motion of a rigid body in a compressible fluid, we only consider the motion of fluid. We especially consider the Navier-Stokes-Korteweg system in the whole space and get the folowing results. We have the global well-posedness in the maximal regularity class around the constant state in the case that the pressure is a strictly increasing function or a constant function of a density.
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| Academic Significance and Societal Importance of the Research Achievements |
近年，Navier-Stokes-Korteweg方程式と剛体双方の運動を記述した問題を解析する数値実験が報告されているが，数学的に方程式の適切性について考察した結果は見当たらない．
また，本研究で用いた時間大域解を得る手法は，Navier-Stokes-Korteweg方程式に限らず，他の放物型方程式や双曲・放物型方程式系を全空間で解析する場合に用いることができると期待される．
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Report
(4 results)
Research Products
(9 results)
