摘要：We first consider a decomposition in L^r of vector fields on 3D bounded domains, which may be regarded as a generalization of the de Rham-Hodge-Kodaira decomposition of differential forms on compact Riemannian manifolds. In accordance with two kinds of boundary conditions, we characterize harmonic vector fields. Our method is based on a certain variational inequality and the generalized Lax-Milgram theorem on the Banach space. Then, we apply our decomposition theorem to the inhomogeneous boundary value problem of the stationary Navier-Stokes equations in multi-connected domains under the general flux condition. This is the joint work with Prof. Taku Yanagisawa at Nara Women University.
演讲人简介：Prof Hideo Kozono，早稻田大学教授。研究Navier-Stokes方程及各种有关方程组、泛函分析、向量场的分析理论。已发表论文110余篇。 2014年获得日本数学会秋季赏（2014 MSJ Autumn Prize），获奖理由是他在不可压Navier-Stokes方程的稳态与非稳态的调和分析研究方面的杰出贡献。