The Equations for the Motion of Viscous Incompressible Fluids

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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]).