Research Keywords: Homogenization Theory, Partial Differential Equations, Fluid Mechanics, Regularity Problems, Boundary Value Problems.
My research lies in fluid mechanics and partial differential equations. In particular, I am interested in qualitative and quantitative homogenization of fluid flows in composite materials and in porous media.
Methods and Techniques such as asymptotic analysis, harmonic analysis and regularity theories are often applied.
The following is the list of my publications and preprints.
Large-scale Regularity of Nearly Incompressible Elasticity in Stochastic Homogenization, (with J. Zhuge)
Arch. Ration. Mech. Anal., 244 (2022), no. 3, 1311-1372. Available at arXiv:2004.14568v2 .
Periodic Homogenization of Green's Functions for Stokes systems, (with J. Zhuge)
Calc. Var. Partial Differential Equations, 58 (2019), no. 3, Art. 114, 46 pp. Available at arXiv:1710.05383v2.
Optimal Boundary Estimates for Stokes Systems in Homogenization Theory, (with Q. Xu)
SIAM J. Math. Anal., 47 (2017), no.5, 3831-3853. Available at arXiv:1612.06042.
Convergence Rates of Neumann Problems for Stokes systems
J. Math. Anal. Appl., 457 (2018), no.1, 305-321. Available at arXiv:1512.08285.
Convergence Rates in Homogenization of Stokes Systems
J. Differential Equations, 260 (2016), no. 7, 5796-5815. Available at arXiv:1508.04203v2.
Homogenization of Stokes Systems and Uniform Regularity Estimates, (with Z. Shen)
SIAM J. Math. Anal., 47-5 (2015), pp.4025-4057. Available at arXiv:1501.03392v2.
Convergence Rates in Homogenization of Non-Stationary Stokes Systems with Time-dependent Coefficients, (with J. Geng)
In preparation.
Homogenization of Stokes Systems with Periodic Coefficients.
Thesis (Ph.D.) University of Kentucky . 2016. 100 pp. ISBN:978-1369-09521-0.