Study on Navier-Stokes equations and related nonlinear partial differential equations

Masuda成功地对二维复形中常高斯曲率的极小曲面进行了完全分类。morimoto证明了具有一般出口边界条件的二维平稳Navier - Stokes方程在通道型对称区域上解的存在性。Konno证明了无界上平方可积函数空间上薛定谔算子的正特征值不存在。Ishimura和Nakamura发现了Kuramoto-Shivashinsky方程的一些重要性质。Tani证明了在一般滑移边界条件下Navier-Stokes方程解的存在性。

Masuda succeeded in classifying completely the minimal surfaces of constant Gaussian curvature in two-dimensional complex formMorimoto showed the existence of solutions of two dimensional stationary Navier Stokes equations with general outlet boundary condition for some symmetric domain of channel type. Konno showed the non-existence of positive eigen-value for Schroedinger operator in the square integrable function space on unbounded domain. Ishimura and Nakamura found some important properties for the Kuramoto-Shivashinsky equations. Tani showed the existence of solutions of Navier-Stokes equations under the general slip boundary conditions.