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<p>We study the global existence of solutions of the three-dimensional Boussinesq equations for rotating stratified fluids in Besov spaces. By striking new balances between the regularizing effects of the dissipations and the dispersive effects caused by the rotation and stratification, we prove existence and uniqueness of global mild solutions to the Cauchy problem and the almost time-periodic problem of 3D Boussinesq equations for rotating stratified fluids under some size conditions, respectively, which permit the initial data and the almost time-periodic external forces to be arbitrarily large, provided that the stratification parameter is large enough. Our results improve the results obtained in Iftimie (Asymptot. Anal. 21, 89-97 (1999)), Lee and Takada (Indiana Univ. Math. J. 66:2037-2070 (2017)) and Hieber et al. (J. Differ. Equ. 266:977-1002, (2019)).</p>

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Global solutions of 3D Boussinesq equations for rotating stratified fluids

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Jinyi Sun,
  • Ning Li,
  • Shengmao Fu

摘要

We study the global existence of solutions of the three-dimensional Boussinesq equations for rotating stratified fluids in Besov spaces. By striking new balances between the regularizing effects of the dissipations and the dispersive effects caused by the rotation and stratification, we prove existence and uniqueness of global mild solutions to the Cauchy problem and the almost time-periodic problem of 3D Boussinesq equations for rotating stratified fluids under some size conditions, respectively, which permit the initial data and the almost time-periodic external forces to be arbitrarily large, provided that the stratification parameter is large enough. Our results improve the results obtained in Iftimie (Asymptot. Anal. 21, 89-97 (1999)), Lee and Takada (Indiana Univ. Math. J. 66:2037-2070 (2017)) and Hieber et al. (J. Differ. Equ. 266:977-1002, (2019)).