Functional-analytic study on incompressible viscous fluid flows

MIYAKAWA对一类非定常Navier-Stokes方程在全空间和半空间中的特定解推导出了用高斯函数表示的时空渐近分布，并将所得结果应用于寻找一般弱解的能量衰减率的下界。HISHIDA考虑绕旋转体的流动。他发展了线性化算子的扰动理论，并将其应用于寻找每一个平方可和初始数据的局部时间解。阿达奇发展了量子多体哈密顿量的谱分析，这些哈密顿量具有类似于上述线性化算符的结构。他的结果涉及到带电和不带电粒子的系统。福山认为问题的发现极限分布离散动力系统所产生的研究缺项三角级数。他推导出一个非高斯极限分布。

MIYAKAWA deduced the space-time asymptotic profiles in terms of some Gaussian functions for a specific class of solutions of nonstationary Navier-Stokes equations in the whole space and the half-space, and then applied the results to finding a lower bound of rates of energy decay for general weak solutions. HISHIDA considered flows around a rotating body. He developed perturbation theory for the linearized operator and applied it to finding local-in-time solutions for every square-summable initial data. ADACHI developed spectral analysis for quantum many-body Hamiltonians which have stuctures similar to the above-mentioned linearized operator. His result is concerned with systems involving charged and uncharged particles. FUKUYAMA considered the problem of finding limit distributions for discrete dynamical systems arising from the study of lacunary trigonometric series. He deduced a non-Gaussian limit distribution.