Speaker: Yuming Qing, doctoral supervisor, Donghua University

Date: December 1, 2023

Time: 15:00-16:00

Location: Tencent Meeting: 803 182 509

Sponsor: School of Mathematics, Shandong University

Abstract:

In this talk, we shall consider the 3D Prandtl equation in a periodic domain and prove the local existence and uniqueness of solutions by the energy method in a polynomial weighted Sobolev space. Compared to the existence and uniqueness of solutions to the classical Prandtl equations where the Crocco transform has always been used with the general outer flow $U\neq\text{constant}$, this Crocco transform is not needed here for 3D Prandtl equations.

We shall use the skill of cancellation mechanism and construct a new unknown function to show that the existence and uniqueness of solutions to 3D Prandtl equations (cf. Masmoudi and Wong, Comm. Pure Appl. Math., 68(10)(2015)，1683-1741) which extends from the two dimensional case in [Y. Qin, X. Wang and J. Liu, Local well-posedness of solutions to 2D magnetic Prandtl model in the Prandt-Hartmann regime, submitted] to the present three dimensional case with a special structure. This work is jointly with Xiuqing Wang.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/185911.htm