中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Liutang Xue（Beijing Normal University）
题 目：Global regularity of non-diffusive temperature fronts for the viscous Boussinesq system
时 间：2022.09.30（星期五）10:00-11:00
地 点：思源楼S315
摘 要：In this talk we address the temperature patch problem of the viscous Boussinesq system with no heat diffusion.
The temperature satisfies the transport equation and the initial data of temperature is given in the form of non-constant patch, usually called the temperature front initial data. By introducing a good unknown and applying the method of the striated estimates initiated by J.-Y. Chemin, we prove that for the initial $C^{k,\gamma}$-regularity of patch boundary with $k\in Z^+$ and $\gamma\in (0,1)$, such a boundary regularity will be persisted by the temperature field for all the time in 2D and in 3D under an additional smallness condition.
This naturally extends the previous work by Gancedo & García-Juárez (2017, 2020) and Danchin & Zhang (2017).
In the proof of the persistence result of higher regularity, we also introduce the striated type Besov spaces and establish a series of fine-scale striated estimates in these function spaces.
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