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题  目:SQG Equation and A Singular Integral

报告人:酒全森 教授

摘  要: The SQG equation (surface quasi-geostrophic equation) is an important model in geophysical flow. In this talk, we will first review some recent results on well-posedness of SQG. Then we will show approximation relations on the smooth solutions between the generalized SQG and the classical SQG. To do that, an uniform estimate to the following singular integral will be applied, which is$$T_jf(x)=K_j*f(x), K_j(x)=\frac{x_j}{|x|^{n+1-\beta}},$$ where $x\in R^n, 0<\beta<n, j=1,2,\cdots, n$. The operator T_j can be viewed as an approximation of the Riesz transform as $\beta\to0$. In particular, we will show that the $(p,p) (p>1)$-type and the weak $(1,1)$-type estimates of the Riesz transform can be recovered from our obtained estimates as $\beta\to 0$.

时  间:2019年6月21日(周五)下午4点10分

地  点:蒙明伟楼1105报告室

邀请人:杨孝平 老师