Xiaoyutao Luo
Academy of Mathematics and Systems Science
About me:
I'm a faculty member at the Morningside Center of Mathematics, Academy of Mathematics and Systems Science in Beijing, China. Here is my CV.
Email: firstname.lastname AT amss.ac.cn
I received my Ph.D. at the University of Illinois at Chicago advised by Alexey Cheskidov in 2020. In 2020-2023, I was a postdoc in the Department of Mathematics at Duke University mentored by Sasha Kiselev.
During 2021-22, I was a member of the IAS for Special Year on h-Principle and Flexibility in Geometry and PDEs.
My current research is focused on PDEs arising from fluid dynamics. See my research footprints below.
Preprints:
Illposedness of incompressible fluids in supercritical Sobolev spaces. arXiv
Eulerian uniqueness of the α-SQG patch problem. arXiv
The α-SQG patch problem is illposed in C^{2,β} and W^{2,p}. (with A. Kiselev) arXiv
Published papers:
Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions. (with A. Cheskidov) to appear in Analysis & PDE 2023. arXiv
Illposedness of C^2 vortex patches. (with A. Kiselev) Arch. Ration. Mech. Anal. 2023. arXiv
On nonexistence of splash singularities for the α-SQG patches. (with A. Kiselev) J. Nonlinear Sci. 2023. arXiv
L^2-critical nonuniqueness for the 2D Navier-Stokes equations. (with A. Cheskidov) Ann. PDE, 2023. arXiv
Sharp nonuniqueness for the Navier-Stokes equations. (with A. Cheskidov), Invent. Math. 2022. arXiv
Anomalous dissipation, anomalous work, and energy balance for the Navier-Stokes equations. (with A. Cheskidov) SIAM J. Math. Anal., 2021. arXiv
Nonuniqueness of weak solutions for the transport equation at critical space regularity. (with A. Cheskidov), Ann. PDE, 2021. arXiv
Energy equality for the Navier-Stokes equations in weak-in-time Onsager spaces. (with A. Cheskidov), Nonlinearity, 2020. arXiv
Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions. Arch. Ration. Mech. Anal., 2019. arXiv
A Beale-Kato-Majda criterion with optimal frequency and temporal localization. J. Math. Fluid Mech, 2019. arXiv
On the possible time singularities for the 3D Navier-Stokes equations. Physica D, 2019. arXiv