【数学与统计及交叉学科前沿论坛------高端学术讲座第175场】

报告题目： Some Results on the Sharp Criteria and Stability for the D-S System with a Defocusing

报 告 人：朱世辉教授 四川师范大学

报告时间：2025年11月27日周四14：00--15:00

报告地点：腾讯会议981-368-544

报告摘要：This talk is concerned with the open problem proposed by Gan and Zhang (Commun. Math. Phys., 283(1), 93-125, 2008) is solved. First,by proposed an ameliorative approach on the basis of the cross-constrained variational argument and profile decomposition theory,the sharp criteria of blow-up and global existence for the Davey-Stewartson system with a defocusing perturbation. Then, the lower bound rate of blow-up solutions for the Davey-Stewartson system is obtained by overcoming the loss of scaling invariance. Finally, a sharp criteria of the existence of stable standing waves is obtained by constructing cross-constraint flows and variational problems. This work joint with Guoyi Fu.

报告人简介：朱世辉，四川师范大学数学科学学院教授、博士生导师，四川省学术和技术带头人后备人选。已主持国家自然科学基金项目3项，教育部博士点基金项目（新教师），四川省杰出青年基金等多个项目。主要从事非线性Schrodinger方程爆破解动力学性质研究，已在JDE，JMP，JDDE，DPDE，中国科学等国内外专业学术刊物上发表论文20余篇。主持项目曾获四川省科技进步三等奖（2022），参与项目曾获四川省科技进步二等奖（2010），四川省高等教育优秀教学成果二等奖（2018）。