Decay estimates of solutions to the compressible micropolar fluids system in R3
Decay estimates of solutions to the compressible micropolar fluids system in R3
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DOI：
10.1016/j.jde.2021.05.038
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发表时间：
2021-08
影响因子：
2.4
通讯作者：
Leilei Tong;R. Pan;Zhong Tan
中科院分区：
文献类型：
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作者：
Leilei Tong;R. Pan;Zhong Tan
这项工作涉及三维空间中的可压缩微极流体系统。当初始摄动足够小时，我们考虑柯西问题解在常平衡态附近的渐近行为。在初始数据的某些假设下，我们证明了柯西问题的解在与线性化方程完全相同的L 2-衰减率下收敛到它的常平衡态，这表明收敛速度是最优的。证明是基于由线性化方程生成的半群的谱分析和非线性能量估计。
This work is concerned with the compressible micropolar fluids system in three–dimensional space. We consider the asymptotic behavior of the solution to the Cauchy problem near the constant equilibrium state provided that the initial perturbation is sufficiently small. Under some assumptions of the initial data, we show that the solution of the Cauchy problem converges to its constant equilibrium state at the exact same L 2–decay rates as the linearized equations, which shows the convergence rates are optimal. The proof is based on the spectral analysis of the semigroup generated by the linearized equations and the nonlinear energy estimates.