1998 Fiscal Year Final Research Report Summary
The Equations for the Motion of Viscous Incompressible Fluids
| Project/Area Number |
09640202
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | Kyushu University |
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Principal Investigator |
KATO Hisako Graduate School of Mathematics, Kyushu University, 大学院・数理学研究科, 教授 (00038457)
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| Co-Investigator(Kenkyū-buntansha) |
HYAKUTAKE Hiroto Graduate School of Mathematics, Kyushu University, Associate Professor, 大学院・数理学研究科, 助教授 (70181120)
ISHIKAWA Nobuhiro Graduate School of Mathematics, Kyushu University, Professor, 大学院・数理学研究科, 教授 (10037806)
NAKAO Mitsuhiro Graduate School of Mathematics, Kyushu University, Professor, 大学院・数理学研究科, 教授 (10037278)
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| Project Period (FY) |
1997 – 1998
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| Keywords | motion of fluids / unique salution / global solution / nonlinear / viscosity / incompressible fluids / velocity gradient / non-Newtonian |
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| Research Abstract |
Head investigator Kato has studied the equations for the motion of viscous incompressible fluids.
1. For the periodicity problem, she proved the existence of periodic solu- tions for the Navier-Stokes equations under critical smallness assumption on the data (Ref. Kato [13).
2. For the initial boundary value problem, she has found modified Navier- Stokes equations, and has proved the existence of global (in time ) strong solutions which satisfy the Navier-Stokes equations in time intervals when the velocity gradient is below a given constant, and satisfy the equations 'called non-Newtonian' in time intervals when the velocity gradient is above the constant (Ref. Kato [2], [3]). Furthermore, she has shown that the solu- tions of the modified Navier-Stokes quations converge to the solutions of the stationary equations as t * *(Ref. Kato [4]).
Investigator Nakao has studied mainly on decay and global existence prob- lems for nonlinear wave equations. Concerning the latter he has derived re- sults which depend on precise decay estimates for energy. He has also derived an interesting result on the decay of local energy for the exterior problem. (Ref. Nakao [1]-[6]).
Investigator Hyakutake gives confidence regions of the multinormal mean by two-stage procedures and its asymptotic properties (Ref. Hyakutake [1], [2]).
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