Communications in Mathematical Sciences

Volume 22 (2024)

Number 5

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

Pages: 1203 – 1250

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n5.a3

Authors

Xinghong Pan (School of Mathematics and Key Laboratory of MIIT, Nanjing University of Aeronautics and Astronautics,Nanjing, China)

Chao-Jiang Xu (School of Mathematics and Key Laboratory of MIIT, Nanjing University of Aeronautics and Astronautics,Nanjing, China)

Abstract

For the three dimensional Prandtl boundary layer equations, we will show that for arbitrary $M$ and sufficiently small $\epsilon$, the lifespan of the Gevrey-2 solution is at least of size $\epsilon^{-M}$ if the initial data lies in suitable Gevrey-2 spaces with size of $\epsilon$.

Keywords

long-time existence, tangentially Gevrey-2 solutions, Prandtl equations

2010 Mathematics Subject Classification

35Q35, 76D03

Full Text (PDF format)

Received 6 December 2022

Received revised 7 October 2023

Accepted 6 November 2023

Published 15 July 2024