SAWADA Okihiro

SAWADA Okihiro
Title Associate Professor      
Department Department of Electrical, Electronic and Computer Engineering 
Course Applied Physics Course

Research fields

My research field is the mathematical analysis of the Navier-Stokes equations and related partial differential equations. The Navier-Stokes equations describe a motion of an incompressible viscous fluid, which is an important, interesting and challenging problem in not only mathematics but also physics, computational science, engineering and economics. So far, none has succeeded to prove the existence of unique solution (or, counter-example) in 3-dimensional problem, which is one of the seven most important open problems in mathematics and has offered a US$1,000,000 prize by The Clay Mathematics Institute. The harmonic analysis (mathematical studies of the Fourier transformation and wavelet) and its application to some partial differential equations for hydrodynamics are also my major field. The threshold between well-posedness and ill-posedness of the Navier-Stokes equations in terms of the function spaces for the initial data has been obtained. One of my specific research was devoted to understand the spin-coat process by the maximal regularity theorem and the method of Newton's polygon.

Research Keywords

Mathematics   Differential Equations   Mathematical Fluid

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