报告题目: Unconditional well-posedness of some dispersive equations and applications

报告人: 霍朝辉 中国科学院数学与系统科学研究院

报告日期：6月26日 星期五

报告时间：9：00-10：00

报告地点：逸夫楼1537

报告摘要：In this talk, we first consider unconditional global well-posedness of the generalized Benjamin-Ono equation without using the gauge transform: ；and the generalized finite-depth-fluid equation；and show that the Cauchy problems of the generalized Benjamin-Ono equation and the generalized finite-depth-fluid equation are unconditionally globally well-posed in with 

Using the above method, we consider the convergence problem for the Benjamin-Ono equation  and show that for with , . Moreover, using the above method, we can consider the uniform convergence of the one-dimensional cubic Schrödinger equation , in with and show that for every .

报告人简介：霍朝辉，博士研究生导师。主要研究方向为偏微分方程与调和分析，运用 Littlewood-Paley 理论、乘子理论、Fourier 限制算子、振荡积分等现代调和分析工具，从事非线性色散波方程相关研究，产出多项标志性学术成果。主持多项国家自然科学基金面上项目。在国内外权威数学期刊发表多篇高水平学术论文，代表性期刊包括：《SIAM, J.Math. Ana.》《Journal de MathématiquesPures et Appliquées》，《Comm. Partial Differential Equations》，《Journal of Differential Equations》，《Forum Math.》《Journal of Geometric Analysis》，《Proceedings of the Edinburgh Mathematical Society》等杂志上。此外，和他人合作完成著作一部《Harmonic Analysis Method for Nonlinear Evolution Equations, I》， World Scientific(2011)。