Yunbai Cao
Hill Assistant Professor
Department of Mathematics
Rutgers University
Email: yc1157@math.rutgers.edu
Office: HLL-544
Research
I am interested in partial differential equations. In particular, I am working on kinetic equations with physical boundary conditions. I'm also interested in the theory of hydrodynamic limits.
Education and Employment
Hill Assistant Professor, Rutgers University-New Brunswick, 2020-
Ph.D. in Department of Mathematics, University of Wisconsin–Madison (Advisor: Chanwoo Kim), 2015-2020
B.S. in Department of Mathematics, University of California, Los Angeles, 2011-2015
Publications
Lipschitz continuous solutions of the Vlasov-Maxwell systems with a conductor boundary condition (C. Kim), submitted. link
Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection, (J.Jang, C.Kim), submitted. link
Rarefied gas dynamics with external fields under specular reflection boundary condition. Accepted in Commun. Math. Sci. link
Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space, (C. Kim). Kinet. Relat. Models 15 (2022), no. 3, 385-401, Special Issue on nonlinear waves and kinetic theory dedicated to the memory of Bob Glassey. Part I. link
On Some Recent Progress in the Vlasov-Poisson-Boltzmann System with Diffuse Reflection Boundary, (C. Kim). In: Salvarani F. (eds) Recent Advances in Kinetic Equations and Applications. Springer INdAM Series, vol 48 (2021). link
A note on two species collisional plasma in bounded domains. Kinet. Relat. Models 12 (2019), no. 6, 1359-1429. link
Regularity of Boltzmann equation with external fields in convex domains of diffuse reflection. SIAM J. Math. Anal. 51 (2019), no. 4, 3195–3275. link
Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains, (C.Kim, D.Lee). Arch. Ration. Mech. Anal. 233 (2019), no. 3, 1027–1130. sharedIt link
Advising caution in studying seasonal oscillations in crime rates, (K. Dong, Y. Cao, B. Siercke, M. Wilber, and S.G. McCalla) PLOS ONE 12(9): e0185432 (2017), link