Members

Xiaoyutao Luo(罗肖雨滔)

Email:xiaoyutao.luo@amss.ac.cn

Office:MCM Building(晨兴楼) 207,Morningside Center of Mathematics, No.55, Zhongguancun East Road, Beijing, 100190, China

Research interest:

partial differential equations

I am currently an associate professor at the Morningside Center of Mathematics, Beijing, China. My current research is focused on PDEs arising from fluid dynamics.

Vitae
(Pre)publications
Teaching
中文版

Education:

2014/08-2020/05 Ph.D University of Illinois at Chicago, US, Supervisor: Alexey Cheskidov

2010/09-2014/06 B.S University of Science and Technology of China

Employment:

2020/08-2023/06 Elliott Assistant Research Professor, Duke University

2021/09-2022/05 Member of the IAS for Special Year on h-Principle and Flexibility in Geometry and PDEs

Preprints:

1. The α-SQG patch problem is illposed in C^{2,β} and W^{2,p}. (with A. Kiselev) arXiv
2. L^2-critical nonuniqueness for the 2D Navier-Stokes equations. (with A. Cheskidov) arXiv accepted by Ann. PDE, 2023.

Publications:
1. Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions. (with A. Cheskidov) to appear in Analysis & PDE 2023 arXiv
2. Illposedness of C^2 vortex patches. (with A. Kiselev) to appear in Arch. Ration. Mech. Anal. 2023 arXiv
3. On nonexistence of splash singularities for the α-SQG patches. (with A. Kiselev) to appear in J. Nonlinear Sci. 2023 arXiv
4. Sharp nonuniqueness for the Navier-Stokes equations. (with A. Cheskidov), Invent. Math. 2022. arXiv
5. Anomalous dissipation, anomalous work, and energy balance for the Navier-Stokes equations. (with A. Cheskidov) SIAM J. Math. Anal., 2021. arXiv
6. Nonuniqueness of weak solutions for the transport equation at critical space regularity. (with A. Cheskidov), Ann. PDE, 2021. arXiv
7. Energy equality for the Navier-Stokes equations in weak-in-time Onsager spaces. (with A. Cheskidov), Nonlinearity, 2020. arXiv
8. Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions. Arch. Ration. Mech. Anal., 2019. arXiv
9. A Beale-Kato-Majda criterion with optimal frequency and temporal localization. J. Math. Fluid Mech, 2019. arXiv

10. On the possible time singularities for the 3D Navier-Stokes equations. Physica D, 2019. arXiv