2015 Fiscal Year Final Research Report
Uniqueness and regularity of solutions to equations in fluid dynamics
| Project/Area Number |
23540194
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | 関数方程式論 / 流体力学 |
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| Outline of Final Research Achievements |
We proved the uniqueness of bounded continuous L_{3,weak}-solutions on the whole time axis to the Navier-Stokes equations in 3-dimensional unbounded domains. Here, L_{3,weak} denotes the weak L_3 space. Thus far, uniqueness of such solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small solution in BC(R;L_{3,weak}) within the class of solutions which have sufficiently small BC(R; L_{3,weak})-norm. In this study, we established another type of uniqueness theorem for solutions in BC(R;L_{3,weak}) using a smallness condition for one solution and a precompact range condition for the other one.
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| Free Research Field |
数学
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