A direct approach to nonuniqueness and failure of compactness for the SQG equation

Nonuniqueness of weak solutions to the SQG equation

We prove that weak solutions of the inviscid SQG equations are not unique, thereby answering Open Problem 11 in the survey arXiv:1111.2700 by De Lellis and Székelyhidi Jr. Moreover, we also show that weak solutions of the dissipative SQG equation are not unique, even if the fractional dissipation is stronger than the square root of the Laplacian.

强制2D纳维-斯托克斯方程和耗散SQG方程的非唯一性

Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations

该研究证明了强制2D纳维-斯托克斯方程和耗散SQG方程在特定条件下的非唯一性结果，揭示了不同类别的解集结构。

关于SQG方程的Onsager猜想的一个证明

A proof of Onsager's Conjecture for the SQG equation

本研究构造了具有最高允许正则性且不守恒哈密顿量的SQG方程解，解决了关于SQG哈密顿守恒阈值正则性的广义Onsager猜想。

哈密顿量紧致性与耗散在无黏极限下的广义SQG方程中

Hamiltonian compactness and dissipation for the generalized SQG equation in the inviscid limit

研究无黏极限下广义SQG方程的耗散机制，通过强紧致性防止哈密顿量异常耗散，揭示更一般的机制，证明在临界积分条件下全局解的存在性。

Global existence for the critical dissipative surface quasi-geostrophic equation

In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in $ \mathbb{R}^2$. Motivated by the study of the homogeneous statistical solutions of this equation, we show that for any large initial data $θ_{0}$ liying in the space $Λ^{s} (\dot H^{s}_{uloc}(\mathbb{R}^2)) \cap L^\infty(\mathbb{R}^2)$ the critical (SQG) has a global weak solution in time for all $1/2< s<1$. Our proof is based on an energy inequality verified by the truncated $(SQG)_{R,\ep}$ equation. By classical compactness arguments, we show that we are able to pass to the limit ($R \rightarrow \…

具有$L^{4/3+}$主动标量的SQG方程的灵活性

Flexibility for the SQG Equation with an $L^{4/3+}$ Active Scalar

该研究针对二维环面上的无粘表面准地转方程，利用凸积分格式在$p=4/3+10^{-5$的主动标量下，证明了弱解的灵活性与非唯一性，拓展了浓度临界指数相关结论。