题    目：The Cauchy problem for the quadratic beam equation in d≥2

主讲人：宋自昊 博士后

单    位：京都大学

时    间：2025年9月27日 9:00

腾讯ID：769-639-669

摘    要：We study the Cauchy problem of the beam equation with quadratic nonlinearity in d≥2. The global well-posedness and scattering of small solutions are established by Strichartz estimates, dispersive estimates and the method of space-time resonance.。The main challenge is to establish the large-time behavior under weak dispersion and bad quadratic nonlinearities. To address these difficulties, we make key observations (1). Null resonance structure in zero frequencies; (2). Separation of source and outcome of space-time resonance. We shall introduce a new frequency decomposition that precisely captures the resonance structure and establish corresponding bilinear estimates of Coifman-Meyer type, which are crucial for overcoming possible degeneracy or loss of derivatives.

简    介：宋自昊, 日本京都大学数理解析研究所博士后，博士后导师ICM报告人Kenji Nakanishi 教授。主要研究方向包括Littlewood-Paley 理论；震荡积分估计理论，Strichartz 估计理论；耗散型可压缩 Navier-Stokes 方程的适定性，Gevrey 解析性，大时间行为研究；色散型可压缩 Euler 方程的适定性，散射行为研究。在Math Ann, JFA, JDE, CVPDE等国际著名数学杂志独立发表多项重要研究工作。