Hisako Kato

On periodic solutions of a semilinear hyperbolic parabolic equation

Uniqueness and regularity of periodic solutions to the semilinear dissipative wave equation with small parameter e > 0, eu tt − Δu + u t + g(u) = f(x, t), on Ω × R and u|∂ Ω = 0, Ω ⊂ R N , are investigated when g(u) has a certain «critical» nonlinearity

Navier-Stokes Equations and Time-Global Strong Solutions

The problem we will consider is the Navier-Stokes initial-boundary value problem. This problem is based on hydrodynamics.

Initial Boundary Value Problem for the Viscous Incompressible Flows

The present paper is concerned with a new model for the viscous incompressible fluids. We propose that the motion of the viscous incompressible fluids is governed by two type equations, namely the Navier-Stokes equations at times when the velocity gradient is below a given constant and the `Ladyzhenskaia equations at times when the velocity gradient is above the constant.