Finite energy solutions to the 6D Fujita equation in the Sobolev critical case
数学专题报告
报告题目(Title)： Finite energy solutions to the 6D Fujita equation in the Sobolev critical case
报告人(Speaker)：Junichi Harada (Akita University)
地点(Place)：Zoom ID: 976 9249 9717, PWD: 816427
时间(Time)：2025 年 5月 8日 16：00-17：00
邀请人(Inviter)：熊金钢
报告摘要
We discuss the dynamics near the ground states for the 6D Fujita equation. This result presents a 6D version of the classification in a higher dimensional setting, obtained by Charles Collot-Frank Merle-Pierre Raphael (2017). In contrast to their results (they assume only that \(u_0\in \dot H^1(\mathbb{R}^n)\)), our result requires the additional integrability conditions on the initial data \(u_0\in L^2(\mathbb{R}^n)\). We also point out that the assumption \(u_0\in \dot H^1(\mathbb{R}^n)\) alone is not sufficient for the stabilization of the solution in the case \(n=6\).
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
