Project/Area Number  09640202 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Kyushu University 
Principal Investigator 
KATO Hisako Graduate School of Mathematics, Kyushu University, 大学院・数理学研究科, 教授 (00038457)

CoInvestigator(Kenkyūbuntansha) 
HYAKUTAKE Hiroto Graduate School of Mathematics, Kyushu University, Associate Professor, 大学院・数理学研究科, 助教授 (70181120)
NAKAO Mitsuhiro Graduate School of Mathematics, Kyushu University, Professor, 大学院・数理学研究科, 教授 (10037278)
ISHIKAWA Nobuhiro Graduate School of Mathematics, Kyushu University, Professor, 大学院・数理学研究科, 教授 (10037806)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,600,000 (Direct Cost : ¥3,600,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥2,300,000 (Direct Cost : ¥2,300,000)

Keywords  motion of fluids / unique salution / global solution / nonlinear / viscosity / incompressible fluids / velocity gradient / nonNewtonian / 流体の運動方程式 / 解の一意性 / 大域解の存在 / 非線形 / 粘性 / 非圧縮流体 / 速度勾配 / 非線形性 / 非圧縮性 
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 NavierStokes 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 NavierStokes equations in time intervals when the velocity gradient is below a given constant, and satisfy the equations 'called nonNewtonian' 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 NavierStokes 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 twostage procedures and its asymptotic properties (Ref. Hyakutake [1], [2]).
