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报告题目： Long-time existence of Gevrey-2 solutions to the 3D Prandtl boundary layer equations

报告人：潘星宏副研究员

报告时间：2023年11月24日下午14：45

报告地点：励学楼B219

报告摘要：We prove the global and almost global existence of small Gevrey-2 solutions to the 3D axially symmetric and full 3D Prandtl equations respectively. The index 2 is the optimal index for well-posedness result in smooth Gevrey function spaces for data without monotonic assumptions. The novelty of our results lies in two aspects: one is the tangentially weighted energy construction to match the r weight in the incompressibility and the other is introducing of the new linearly good unknowns to obtain the fast decay of the lower order Gevrey-2 norms of the solutions and auxiliary functions. The results are based on joint work with Professor Chao-Jiang Xu.

报告人简介：潘星宏，南京航空航天大学副研究员。2017年3月毕业于南京大学数学系，取得理学博士学位。 读博期间于2014年12月至2016年12月赴加州大学河滨分校进行博士联合培养。入选2018年江苏省“双创博士”人才计划，主持江苏省自然科学基金青年基金和国家自然科学基金青年基金各一项, 参与重点项目一项。主要研究方向为Navier-Stokes方程解的适定性问题，目前，在 Arch. Ration. Mech. Anal.，J. Funct. Anal., J. Differential Equations, Calc. Var. Partial Differential Equations, Commun. Contemp. Math.等杂志发表多篇SCI论文。