Research for Critical Asymptotic Structure of Nonlinear Evolution Equations

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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.