Research

My main research interests are energy minimization and related dynamical problems, including gradient flows and other models from collective dynamics. I’m also interested in numerical methods for kinetic and hyperbolic problems.

Selected publications:

[21] Ruiwen Shu and Jiuya Wang, Generalized Erdős-Turán inequalities and stability of energy minimizers, preprint.

[20] Ruiwen Shu and Jiuya Wang, The sharp Erdős-Turán inequality, preprint.

[19] José A. Carrillo and Ruiwen Shu, From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials, preprint.

[18] Mingchang Ding, Jing-Mei Qiu and Ruiwen Shu, Accuracy and stability analysis of the Semi-Lagrangian method for stiff hyperbolic relaxation systems and kinetic BGK model, preprint.

[17] Mingchang Ding, Jing-Mei Qiu and Ruiwen Shu, Semi-Lagrangian nodal discontinuous Galerkin method for the BGK Model, preprint.

[16] Sigal Gottlieb, Zachary Grant, Jingwei Hu and Ruiwen Shu, High order unconditionally strong stability preserving multi-derivative implicit and IMEX Runge-Kutta methods with asymptotic preserving properties, SIAM Numer. Anal., accepted.

[15] Douglas Hardin, Edward Saff, Ruiwen Shu and Eitan Tadmor, Dynamics of particles on a curve with pairwise hyper-singular repulsion, Discrete Contin. Dyn. Syst., accepted.

[14] Ruiwen Shu and Eitan Tadmor, Newtonian repulsion and radial confinement: convergence towards steady state, Mathematical Models and Methods in Applied Sciences, 1-25, 2021.

[13] Ruiwen Shu, Tightness of radially-symmetric solutions to 2D aggregation-diffusion equations with weak interaction forces, preprint.

[12] Ruiwen Shu, Equilibration of aggregation-diffusion equations with weak interaction forces, SIAM J. Math. Anal., accepted.

[11] Jingwei Hu and Ruiwen Shu, On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations, Mathematics of Computation, 90: 641-670, 2021.

[10] Ruiwen Shu and Eitan Tadmor, Anticipation breeds alignment, Archive for Rational Mechanics and Analysis, 240(1): 203-241, 2021.

[9] Jingwei Hu, Shi Jin and Ruiwen Shu, On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime, J. Comput. Phys., 397: 108838, 2019.

[8] Ruiwen Shu and Eitan Tadmor, Flocking hydrodynamics with external potentials, Archive for Rational Mechanics and Analysis, 2020: 1-35.

[7] Jingwei Hu and Ruiwen Shu, A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations, SIAM Multiscale Model. Simul., 17(4): 1123-1146, 2019.

[6] Ruiwen Shu and Shi Jin, A study of Landau damping with random initial inputs, J. Differ. Equat., 266(4): 1922-1945, 2019.

[5] Jingwei Hu, Ruiwen Shu and Xiangxiong Zhang, Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation, SIAM J. Numer. Anal., 56(2): 942-973, 2018.

[4] Qin Li, Jian-Guo Liu and Ruiwen Shu, Sensitivity analysis of Burgers’ equation with shocks, SIAM/ASA J. Uncertainty Quantification, 8(4): 1493-1521, 2020.

[3] Qin Li, Ruiwen Shu and Li Wang, A new numerical approach to inverse transport equation with error analysis, SIAM J. Numer. Anal., 56(6): 3358-3385, 2018.

[2] Ruiwen Shu and Shi Jin, Uniform regularity in the random space and spectral accuracy of the stochastic Galerkin method for a kinetic-fluid two-phase flow model with random initial inputs in the light particle regime, ESAIM Math. Model. Numer. Anal., 52(5): 1651-1678, 2018.

[1] Shi Jin and Ruiwen Shu, A stochastic Asymptotic-Preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty, J. Comput. Phys., 335: 905-924, 2017.