Global Existence for the Semi-Dissipative 2D Boussinesq Equations on Exterior Domains

Ruili Wu, Lunzhong Guo and Junyan Li ()
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Ruili Wu: School of Big Data and Artificial Intelligence, Chengdu Technological University, Zhongxin Street, Chengdu 611730, China
Lunzhong Guo: School of Big Data and Artificial Intelligence, Chengdu Technological University, Zhongxin Street, Chengdu 611730, China
Junyan Li: Department of Mathematics, Chengdu Jincheng College, Xiyuan Street, Chengdu 611731, China

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: This paper concerns the viscous Boussinesq equations without a dissipation term and their relation to the temperature equation related to the exterior of a ball with a smooth boundary. We first prove the global existence of weak solutions on the bounded domain Ω ˜ via the Schauder fixed-point theorem. Then, we derive the uniform estimates to obtain the global existence of weak solutions on the unbounded domain Ω by utilizing the domain expansion method. Finally, we show that the equations have a unique classical solution for H 3 initial data by a series of regularity estimations.

Keywords: Boussinesq equations; Schauder fixed-point theorem; domain expansion method; classical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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