Xiaoyutao Luo
Academy of Mathematics and Systems Science
Xiaoyutao Luo
Academy of Mathematics and Systems Science
I'm a faculty member at the Morningside Center of Mathematics and the Academy of Mathematics and Systems Science in Beijing. Here is my CV.
Email: firstname.lastname AT amss.ac.cn
I received my Ph.D. from the University of Illinois at Chicago, advised by Alexey Cheskidov in 2020. In 2020-2023, I was a postdoc at Duke University, mentored by Sasha Kiselev. I arrived at MCM & AMSS in July 2023.
My current research is focused on PDEs arising from fluid dynamics. See my research footprints below.
Long time inviscid damping near Couette in Sobolev spaces. (with D. Guo) arXiv
Sharp norm inflation for 3D Navier-Stokes equations in supercritical spaces. arXiv
Eulerian uniqueness of the α-SQG patch problem. arXiv
Illposedness of incompressible fluids in supercritical Sobolev spaces. to appear in Duke arXiv
The α-SQG patch problem is illposed in C^{2,β} and W^{2,p}. (with A. Kiselev) CPAM 2024. arXiv
Illposedness of C^2 vortex patches. (with A. Kiselev) Arch. Ration. Mech. Anal. 2023. arXiv
Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions. (with A. Cheskidov) Analysis & PDE 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