Zhuolun Yang
Personal Info
I am a Prager Assistant Professor (postdoc position) at Division of Applied Math, Brown University. My mentor is Hongjie Dong. I received my Ph.D. at Rutgers University in 2021 under the supervision of Yanyan Li. You may find my CV here.
Contact Info
182 George Street, Room 323, Providence, RI 02912.
Office hours for Spring 2025: Mondays 4 pm - 5 pm, Fridays 4:30 pm - 5:30 pm.
Email address: zhuolun_yang at brown dot edu
Research
My research interests lie in analysis, partial differential equations, and fluid dynamics. My current research focuses on the regularity of elliptic equations/systems, high-contrast composite materials, and the Navier-Stokes equation. I am open to learning and engaging in different directions within the field of PDEs.
I am co-organizing the Brown PDE seminar.
Published or accepted papers:
Gradient estimates for the insulated conductivity problem: The non-umbilical case (With H.Dong and Y.Y.Li). J. Math. Pures Appl. 189 (2024), 103587. [arXiv] [Journal]
Asymptotics of the solution to the perfect conductivity problem with p-Laplacian (With H.Dong and H.Zhu). Math. Ann. 390 (2024), no. 4, 5005-5051. [arXiv] [Journal]
Optimal gradient estimates of solutions to the insulated conductivity problem in dimensions greater than two (With H.Dong and Y.Y.Li). J. Eur. Math. Soc. (2024). [arXiv] [Journal]
The insulated conductivity problem with p-Laplacian (With H.Dong and H.Zhu). Arch. Ration. Mech. Anal. 247 (2023), 95 [arXiv] [Journal]
Optimal estimates for transmission problems including relative conductivities with different signs (With H.Dong). Adv. Math. 428 (2023), 109160. [arXiv] [Journal]
Gradient estimates of solutions to the insulated conductivity problem in dimensions greater than two (With Y.Y.Li). Math. Ann. 385 (2023), no. 3-4, 1775–1796. [arXiv] [Journal]
Regular solutions of the stationary Navier-Stokes equations on high dimensional Euclidean space (With Y.Y.Li). Commun. Math. Phys. 394 (2022), no. 2, 711–734. [arXiv] [Journal]
Gradient estimates of solutions to the conductivity problem with flatter insulators (With Y.Y.Li). Anal. Theory Appl. 37 (2021), no. 1, 114-128. [Journal]
Asymptotics of the gradient of solutions to the perfect conductivity problem (With H.G.Li and Y.Y.Li). Multiscale Model. Simul. 17 (2019), no. 3, 899-925. [arXiv] [Journal]
Preprints:
Small scales in inviscid limits of steady fluids (With Y.Guo). arXiv:2409.09604. [arXiv]
Gradient estimates for the conductivity problem with imperfect bonding interfaces (With H.Dong and H.Zhu). arXiv:2409.05652. [arXiv]
Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier-Stokes Equation in R^3 (With J.Bang). arXiv:2402.11144. [arXiv]