| Project/Area Number |
15K04946
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
Takayuki Kubo 筑波大学, 数理物質系, 講師 (90424811)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
高安 亮紀 筑波大学, システム情報系, 助教 (60707743)
|
|---|
| Project Period (FY) |
2015-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | Navier-Stokes方程式 / 重み付き空間 / 二相問題 / 最大正則性定理 / Stokes半群のLp-Lq評価 / 最大正則性 / 圧力安定化法 / 弱解 / 時間局所解 / 定常解 / 2次元半空間 / 最大正則性原理 / ２次元半空間 / 自由境界問題 / 安定性 |
|---|
| Outline of Final Research Achievements |
We derived the weighted Lp-Lq estimates of Stokes semigroups in some unbounded domains in weighted Lp space such as inhomoginuous weights, and obtained the decay estimate at time infinity in that space. In a similar method, we obtained the local energy decay estimate for the exterior domain of the hyperbolic Navier-Stokes equations.
For the compressible-compressible two-phase problems, we derived R-boundedness for the solution operator of the linearized problem of model problems. For the bounded domain, we could show the unique existence of local in time solutions for arbitrary initial values. In order to consider the computer-assisted proof for the nonexistent range of the eigenvalues, we considered the approximation problem by the pressure stabilization method and showed the validity of the approximation.
|
| Academic Significance and Societal Importance of the Research Achievements |
重み付き空間での解析は，定常問題の安定性解析に有用であり意義がある．また，方向別に重みを変えることができるのはこれから多くの応用が期待できる．
二相問題についての結果や圧力安定化法の近似の正当性に関する結果は，自由境界問題や流体運動のシミュレーションの結果を数学的に保証するものであり，とても意義のある結果である．
|
