Xukai Yan

Contact Information
Department of Mathematics Oklahoma State University 401 Mathematical Sciences, Stillwater, OK 74078 Office: MSCS 441 Office phone: (405)7445698 Fall 2022 Teaching: Math 2233, Differential Equations Office hours: Mon & Wed 3:30 - 5:00 p.m. E-mail: xuyan [at] okstate.edu

About Me
I am an assistant professor at Department of Mathematics, Oklahoma State University. I am interested in partial differential equations and nonlinear analysis. Here is my CV. Before coming to OSU, I was a postdoc at Georgia Tech, and my mentors are Ronghua Pan and Yao Yao. I got my Ph.D. degree in May 2017 from Rutgers University, under the supervision of Yanyan Li.

Research

Homogeneous solutions of stationary Navier-Stokes equations with isolated sigularities on the unit sphere. I. One sigularity, with Y. Y. Li and L. Li , Arch. Ration. Mech. Anal. , 227 (2018), 1091-1161.

Homogeneous solutions of stationary Navier-Stokes equations with isolated sigularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions, with Y. Y. Li and L. Li, Journal of Differential Equations , 264 (2018), 6082-6108.

Vanishing viscosity limit for homogeneous axisymmetric no-swirl solutions of stationary Navier-Stokes equations, with Y. Y. Li and L. Li, Journal of Functional Analysis , 227 (2019), 3599-3652.

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two Singularities, with Y. Y. Li and L. Li, Discrete and Continuous Dynamical Systems - Series A , 39 (2019), 7163-7211.

Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations, with M. G. Delgadino and Y. Yao, Comm. Pure Appl. Math. 75 (2022), 3-59.

Symmetry of hypersurfaces with ordered mean curvature in one direction, with Y. Y. Li and Y. Yao, Calc. Var. PDE. 60, 173 (2021).

Asymptotic stability of homogeneous solutions to the Navier-Stokes equations in R^3, with Y. Y. Li, Journal of Differential Equations, 297 (2021), 226-245.

Sharp stability of interaction energy, with Y. Yao, Arch. Ration. Mech. Anal. (2022) available online (https://doi.org/10.1007/s00205-022-01823-y), arXiv:2009. 07502 [math.AP].

Anisotropic Caffarelli-Kohn-Nirenberg type inequalities, with Y. Y. Li, submitted, arXiv:2112.00217 [math.AP] .