primitive equations
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Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 165
Author(s):  
Muhammad Zainul Abidin ◽  
Naeem Ullah ◽  
Omer Abdalrhman Omer

We consider the Cauchy problem of the three-dimensional primitive equations of geophysics. By using the Littlewood–Paley decomposition theory and Fourier localization technique, we prove the global well-posedness for the Cauchy problem with the Prandtl number P=1 in variable exponent Fourier–Besov spaces for small initial data in these spaces. In addition, we prove the Gevrey class regularity of the solution. For the primitive equations of geophysics, our results can be considered as a symmetry in variable exponent Fourier–Besov spaces.


Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1961
Author(s):  
Yuanfei Li ◽  
Peng Zeng

In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice.


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