Research for Critical Asymptotic Structure of Nonlinear Evolution Equations

主要研究者T. Ogawa研究了几个具有临界结构的非线性偏微分方程，发现了每个问题的不同临界性。他与合作者一起研究了以下主题。临界Besov空间中的二维漂移扩散系统，建立了非自反Banach空间中热方程的极大正则性。高空间维漂移扩散系统解的高阶展开，非线性阻尼波系统的整体存在性，对数型临界Sobolev不等式及其在抽象Besov空间的推广，非线性薛定谔方程与泊松方程的WKB近似，二次非线性薛定谔方程的标度临界可解性和低空间维的临界适定性。

The main reseacher T. Ogawa researched several nonlinear partial differential equations with critical structure and find various criticality in each problems. He studied the following topics with colabolators. Two dimensional drift-diffusion system in the critical Besov spaces and established maximal regularity for the heat equation in non-reflexivie Banach spaces. Higher order expansion of the solution for the drift-diffusion system in higher space dimensions, the global existence for the nonlinear damped wave system, the critical Sobolev inequality with logarithmic type and generalization to abstract Besov spaces, WKB approximation for nonlinear Schrodinger equations with Poisson equations, the scaling critical solvabilityfor quadratic nonlinear Schrodinger equation and critical well-posedeness in lower space dimensions.