My research interests include energy minimization problems and related gradient flows, collective dynamics, numerical methods for kinetic and hyperbolic problems, and uncertainty quantification.

My publications:

[19] Douglas Hardin, Edward Saff, Ruiwen Shu and Eitan Tadmor, Dynamics of particles on a curve with pairwise hyper-singular repulsion, submitted.

[18] Ruiwen Shu and Eitan Tadmor, Newtonian repulsion and radial confinement: convergence towards steady state, submitted.

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

[16] Ruiwen Shu, Equilibration of aggregation-diffusion equations with weak interaction forces, submitted. (See an updated version)

[15] 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, to appear.

[14] Shi Jin and Ruiwen Shu, Collective dynamics of opposing groups with stochastic communication, Vietnam Journal of Mathematics, 2020: 1-18.

[13] Ruiwen Shu and Eitan Tadmor, Anticipation breeds alignment, submitted.

[12] 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.

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

[10] Shi Jin and Ruiwen Shu, A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty, Chinese Annals of Mathematics, Series B, 40(5), 765-780, 2019.

[9] 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.

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

[7] 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.

[6] Qin Li, Jian-Guo Liu and Ruiwen Shu, Sensitivity analysis of Burgers’ equation with shocks, SIAM/ASA J. Uncertainty Quantification, to appear.

[5] 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.

[4] 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.

[3] Jingwei Hu, Shi Jin and Ruiwen Shu, * A stochastic Galerkin method for the Fokker-Planck-Landau equation with random uncertainties, * Proc. 16th Int’l Conf. on Hyperbolic Problems, pp. 1-19, 2016. 3

[2] Ruiwen Shu, Jingwei Hu and Shi Jin, * A Stochastic Galerkin Method for the Boltzmann Equation with multi-dimensional random inputs using sparse wavelet bases, * Numer. Math. Theor. Meth. Appl. (NMTMA) 10, 465-488, 2017. (A special issue in honor of the 80th birthday of Prof. Zhenhuan Teng) 1 2

[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.