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

  1. Lipschitz continuous solutions of the Vlasov-Maxwell systems with a conductor boundary condition (C. Kim), submitted. link

  2. Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection, (J.Jang, C.Kim), submitted. link

  3. Rarefied gas dynamics with external fields under specular reflection boundary condition. Accepted in Commun. Math. Sci. link

  4. 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

  5. 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

  6. A note on two species collisional plasma in bounded domains. Kinet. Relat. Models 12 (2019), no. 6, 1359-1429. link

  7. Regularity of Boltzmann equation with external fields in convex domains of diffuse reflection. SIAM J. Math. Anal. 51 (2019), no. 4, 3195–3275. link

  8. 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

  9. 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

CV.pdf