2011 Fiscal Year Final Research Report
Study on half-space problem for non-linear PDE in Fluid Dynamics and its application
| Project/Area Number |
21740105
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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 | University of Tsukuba |
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Principal Investigator |
KUBO Takayuki 筑波大学, 数理物質系, 助教 (90424811)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 関数方程式 / 流体力学 |
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| Research Abstract |
In this study, we studied analysis of weighted Lp space of Navier-Stokes equation, which is the basic equation of fluid dynamics. As a result, if the weight function belongs to the Muckenhoupt weight class, we are able to prove the weighted Lp-Lq estimates of Stokes semigroup in exterior domains, half-spaces and perturbed half spaces. Moreover we could also show the unique existence of the solution to the Navier-Stokes equations and its asymptotic behavior in weighted Lp framework.
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