Zihui He
Postdoctoral researcher at Bielefeld University
I am a postdoctoral researcher in the Faculty of Mathematics at Bielefeld University with Prof. Matthias Erbar. Previously, I was a Ph.D. student in the Institute for Analysis at Karlsruhe Institute of Technology under the supervision of JProf. Xian Liao.
Email: zihui.he@uni-bielefeld.de
Office: V4-238
Address:
Universität BielefeldFakultät für MathematikPostfach 10013133501 Bielefeld, GermanyResearch interests: Nonlinear PDEs, Boltzmann equations, Navier-Stokes equations
Upcoming events: I am co-organizing the mini-symposium ''(In-)Stability, Dispersion and Weak Turbulence: From Fluid Flow to Hamiltonian Systems'' with Lars Eric Hientzsch (Bielefeld) and Tobias Schmid (EPFL) at the Conference on Mathematics of Wave Phenomena, February 24-28, 2025, Karlsruhe
Publications and preprints:
Convergence of fuzzy Boltzmann equations to inhomogeneous Boltzmann equations.
Joint work with Matthias Erbar, in preparation.
A variational approach to a fuzzy Boltzmann equation.
Joint work with Matthias Erbar, preprint, arxiv:2404.12032
Three-dimensional stationary incompressible inhomogeneous Navier-Stokes equation in the axially symmetric case.
Preprint, arxiv:2212.14423
Solvability of the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with variable viscosity coefficient.
Joint work with Xian Liao, Commun. Contemp. Math. (2024)
www.worldscientific.com/doi/10.1142/S0219199723500396
Turbulent cascades for a family of damped Szegö equations.
Joint work with Patrick Gérard and Sandrine Grellier, Nonlinearity (2022)
https://iopscience.iop.org/article/10.1088/1361-6544/ac7e13
On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusion.
Joint work with Xian Liao, Zeitschrift für angewandte Mathematik und Physik (2022)
Teaching:
Bielefeld University
Seminar: Variational Structures for Dissipative PDEs, summer 2024, with Matthias Erbar
Seminar: Optimal transport and Applications, winter 2022/23, with Matthias Erbar and Timo Schultz
Karlsruhe Institute of Technology
Teaching assistant (Tutorial classes, homework assignments, exams organization)
Fourier analysis and its applications to PDEs, winter 2021/22
Boundary and Eigenvalue Problems, summer 2021 (in German)
Classical Methods for Partial Differential Equations, winter 2020/21 (in German)
Boundary and Eigenvalue Problems, summer 2020
Classical Methods for Partial Differential Equations, winter 2019/20
Fourier analysis and its applications to PDEs, summer 2019
Dispersive equations, winter 2018/19