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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ruili Wu & Lunzhong Guo & Junyan Li, 2025. "Global Existence for the Semi-Dissipative 2D Boussinesq Equations on Exterior Domains," Mathematics, MDPI, vol. 13(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:369-:d:1574718
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