Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (2): 616-627.

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Long-Time Well-Posedness of the Hyperbolic Prandtl Equations in Gevrey Spaces

Weixi Li*(), Jiaxi Wang(), Zhan Xu()   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2025-12-22 Revised:2026-01-27 Online:2026-04-26 Published:2026-04-27
  • Contact: Weixi Li E-mail:wei-xi.li@whu.edu.cn;wangjiaxi@whu.edu.cn;xuzhan@whu.edu.cn
  • Supported by:
    NSFC(12325108);NSFC(12131017);NSFC(12221001);Natural Science Foundation of Hubei Province(2019CFA007)

Abstract:

In this paper, we investigate the 2D and 3D hyperbolic Prandtl equations. We prove that this system has a unique long-time solution with small initial data in Gevrey function space with index up to 2. The proof is based on a new cancellation mechanism with linear terms and the decay rate of the radius with respect to time.

Key words: hyperbolic Prandtl equations, Gevrey spaces, long-time well-posedness

CLC Number: 

  • O175.23
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