Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 62, pp. 1-16.

Title: Global classical solutions to equatorial shallow-water equations
       
Authors: Yue Fang (Ocean Univ. of China, Qingdao, China)
         Kaiqiang Li (Yantai Univ., Yantai, China)
         Xin Xu  (Ocean Univ. of China, Qingdao, China)
         
Abstract: 
In this article, we study the equatorial shallow-water equations with slip boundary condition in a bounded domain. By exploring the dissipative 
structures of the system,  we obtaining a priori estimates of the solution 
for small initial data. 
Then the existence of classical global solutions and exponential stability results are given.

Submitted April 20, 2023. Published September 21, 2023.
Math Subject Classifications: 35Q35, 76N10, 76U05, 76M45.
Key Words: Equatorial shallow-water equations; global classical solution; exponential stability.