部分耗散的三维Boussinesq方程在静力平衡附近的稳定性和指数衰减

Abstract

Abstract:

This paper is devoted to solving the stability and large time behavior problem on three dimensional Boussinesq equations with anisotropic dissipation and vertical thermal diffusion near the hydrostatic equilibrium. The stability of the solution with certain symmetries to the Boussinesq euations is established on the spatial domain $R^2\times \mathrm{T}$ with the periodic box $\mathrm{T}=[-\frac12,\frac12]$. In addition, the oscillators of the velocity $u$ and the temperature $\theta$ admit the exponential decay in time variable $t$.

Key words: Boussinesq equations, Stability, Hydrostatic equilibrium, Large-time behavior

CLC Number:

O175.27

Li Xiaoli,Chen Xiaoli. Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation[J].Acta mathematica scientia,Series A, 2023, 43(3): 754-770.

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References

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Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation

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