報告題目： Long-time existence of Gevrey-2 solutions to the 3D Prandtl boundary layer equations

報告人：潘星宏副研究員

報告時間：2023年11月24日下午14：45

報告地點：勵學樓B219

報告摘要：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.

報告人簡介：潘星宏，南京航空航天大學副研究員。2017年3月畢業于南京大學數學系，取得理學博士學位。 讀博期間于2014年12月至2016年12月赴加州大學河濱分校進行博士聯合培養。入選2018年江蘇省“雙創博士”人才計劃，主持江蘇省自然科學基金青年基金和國家自然科學基金青年基金各一項, 參與重點項目一項。主要研究方向為Navier-Stokes方程解的适定性問題，目前，在 Arch. Ration. Mech. Anal.，J. Funct. Anal., J. Differential Equations, Calc. Var. Partial Differential Equations, Commun. Contemp. Math.等雜志發表多篇SCI論文。