Global well-posedness for the 3D rotating Boussinesq equations in variable exponent Fourier-Besov spaces

Xiaochun Sun; Yulian Wu; Gaoting Xu; Xiaochun Sun; Yulian Wu; Gaoting Xu

doi:10.3934/math.20231385

AIMS Mathematics

2023, Volume 8, Issue 11: 27065-27079. doi: 10.3934/math.20231385

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Research article

Global well-posedness for the 3D rotating Boussinesq equations in variable exponent Fourier-Besov spaces

Collage of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 07 August 2023 Revised: 07 September 2023 Accepted: 13 September 2023 Published: 25 September 2023
MSC : 35A01, 35Q35, 35Q86, 76U05

We study the small initial data Cauchy problem for the three-dimensional Boussinesq equations with the Coriolis force in variable exponent Fourier-Besov spaces. Using the Fourier localization argument and Littlewood-Paley decomposition, we obtain the global well-posedness result for small initial data $ (u_0, \theta_0) $ belonging to the critical variable exponent Fourier-Besov spaces $ \mathcal{F}\mathcal{\dot{B}}_{p(\cdot), q}^{2-\frac{3}{p(\cdot)}} $.
- Boussinesq equations,
- Coriolis force,
- global well-posedness,
- variable exponent Fourier-Besov spaces
Citation: Xiaochun Sun, Yulian Wu, Gaoting Xu. Global well-posedness for the 3D rotating Boussinesq equations in variable exponent Fourier-Besov spaces[J]. AIMS Mathematics, 2023, 8(11): 27065-27079. doi: 10.3934/math.20231385

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Abstract

We study the small initial data Cauchy problem for the three-dimensional Boussinesq equations with the Coriolis force in variable exponent Fourier-Besov spaces. Using the Fourier localization argument and Littlewood-Paley decomposition, we obtain the global well-posedness result for small initial data $ (u_0, \theta_0) $ belonging to the critical variable exponent Fourier-Besov spaces $ \mathcal{F}\mathcal{\dot{B}}_{p(\cdot), q}^{2-\frac{3}{p(\cdot)}} $.

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