Uniqueness of weak solutions to the Boussinesq equations with fractional dissipation
Uniqueness of weak solutions to the Boussinesq equations with fractional dissipation
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DOI：
10.4310/cms.2023.v21.n6.a4
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发表时间：
2023
影响因子：
1
通讯作者：
Ruihong Ji;Dan Li;Jiahong Wu
中科院分区：
文献类型：
--
作者：
Ruihong Ji;Dan Li;Jiahong Wu
。本文研究了具有分数阶耗散项(−∆)αu)和分数阶热扩散项(−∆)βθ.目的是在最弱可能的非齐次Besov空间中证明弱解的唯一性。我们证明了函数环境u∈L∞(0，T；Bd/2−2α+1 2，1(Rd))和θ∈L∞(0，T；Bd/2 2，1(Rd))在α>；1/4，β≥0和α+2β≥1时的局部存在唯一性。通过将双线性项分解成不同的频率，我们得到了双线性项的一个合适的上界，这使得我们可以关闭上述Besov空间中的估计。
. This paper examines the existence and uniqueness of weak solutions to the d-dimensional Boussinesq equations with fractional dissipation ( − ∆) α u and fractional thermal diffusion ( − ∆) β θ . The aim is at the uniqueness of weak solutions in the weakest possible inhomogeneous Besov spaces. We establish the local existence and uniqueness in the functional setting u ∈ L ∞ (0 ,T ; B d/ 2 − 2 α +1 2 , 1 ( R d )) and θ ∈ L ∞ (0 ,T ; B d/ 2 2 , 1 ( R d )) when α> 1 / 4, β ≥ 0 and α +2 β ≥ 1. By de-composing the bilinear term into different frequencies, we are able to obtain a suitable upper bound on the bilinear term, which allows us to close the estimates in the aforementioned Besov spaces.