SAWADA, Okihiro:COE Research Fellow,Analysis

Navier-Stokes equations, harmonic analysis
Research Interest:
Partial Differential Equations
Research Activities:
I mainly consider the incompressible viscous flow of the ideal fluid, described by a system of the Navier-Stokes equations. In particular, my interests are to establish the theory of the existence of local-in-time smooth solutions and properties of obtained solutions (uniqueness, regularity, analyticity). We employ the recent development of harmonic analysis and semigroup theory, and sometimes create new tools. One of the purposes of this research is to investigate the border of the local-in-time well-posedness or ill-posedness of the Navier-Stokes problem. It is also interesting to discuss the stability or instability of steady flows, observing the nonstationary flows near the stationary solutions. I also study the Bouseinesq equations (concerning the heat convection), the semi-linear heat equation (a model of combustion), and the Keller-Segel equations (a model of cell movement of mycetozoan by chemotaxis). I am interested in the virtue of solutions, particularly, regularity and analyticity. Very recently, I try to obtain the mathematical results on the motion of incompressible viscous fluid on a rotating disc, which illustrate the spin-coating-process (the adhesion of thin film).