We study the well-posedness of a hyperbolic quasi-linear version of hydrostatic Navier–Stokes system in \(\mathbb R\times \mathbb T\) and prove the global well-posedness of the system with initial data which are small and analytic in both variables. We also prove the convergence of such analytic solutions to that of the classical hydrostatic Navier–Stokes system when the delay time converges to zero. Furthermore, we obtain a local well-posedness result in Gevrey class 2 when the initial datum is a small perturbation of some convex function. 

Publication: 

SIAM Journal on Mathematical Analysis, Vol. 55, Iss. 6 (2023) 

https://doi.org/10.1137/22M1526290 

Author: 

Wei-Xi Li 

School of Mathematics and Statistics, Wuhan University, 430072, Wuhan, China 

Computational Science, Hubei Key Laboratory, Wuhan University, 430072, Wuhan, China. 

Marius Paicu 

Université Bordeaux, Institut de Mathématiques de Bordeaux, F-33405 Talence Cedex, France. 

Ping Zhang 

Academy of Mathematics, Systems Science, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China 

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China. 

Email: zp@amss.ac.cn