Xiongtao Zhang

Professors:Xiongtao Zhang

Name:Xiongtao Zhang
Title:Associate professor
Kinectic dynamics,Hyperbolic partial differential equations, collective dynamics of complex systems, particle dynamics and mean-field theory.
Educational background:
• B.S. Mathematics, Wuhan University, July 2009.
• Ph.D. Mathematics, National University of Singapore, July 2014.
– Thesis Title: On Rayleigh wave and Lamb’s problem
– Thesis Advisor : Prof. Shih-Hsien Yu.
Work experience:
• Teaching Assistant, Department of Mathematics,National University of Singapore, 2010. 8 – 2013. 7.
– Tutor of subject: Calculus, Discrete Structure and Partial Differential Equations.
– Grader of subject: Calculus, Financial Mathematics, Algebra, Analysis.
• Research Assistant (Part-time), Department of Mathematics, National University of Singapore, 2013. 8 – 2014. 7.
Research fields:
• Boundary effects and surface wave in hyperbolic systems.
• Asymptotic behaviors on the dynamical systems describing emergent phenomena, which arises from the engineering , physical and biological applications (e.g. Kuramoto model, Winfree model, Cucker-Smale model, etc.).
• Derivability of kinetic equation from particle system with or without noise: uniform mean-field limit and uniform stability of particle system and correspondingasymptotical behavior of measure valued solution.
• Well-posedness of the solutions to kinetic equations and kinetic-fluid coupled system: Vlasov-type equation (e.g. Kinetic Cucker-Smale model, Kinetic Kuramotomodel, Kinetic Winfree model, etc.), Vlasov-Fokker-Planck equation (e.g. Kinetic Cucker-Smale model with diffusion).
Scientific achievements:
• Emergent dynamics in the interactions of Cucker-Smale ensembles (with S.-Y. Ha, D. Ko and Y. Zhang). To appear in Kinetic and Related Models.
• Collective synchronization of classical and quantum oscillators (with S.-Y. Ha, D. Ko and J. Park). EMS Surv. Math. Sci. 3 (2016), no. 2, 209–267.
• Emergent Dynamics of Cucker-Smale flocking particles in a random environment(with S.-Y. Ha, S. E. Noh, J. Jeong, Q. Xiao).J. Differential Equations 262 (2017), no. 3, 2554–2591.
• Time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles (with S.-Y. Ha, D. Ko and Y. Zhang). submitted.
• Uniform stability of the Cucker-Smale model and its applicaiton to the mean-field limit (with S.-Y. Ha and J. Kim). submitted.
• Emergent dynamics of Cucker–Smale particles under the effects of random communication and incompressible fluids (with S.-Y. Ha and Q. Xiao) submitted
• A global well-posedness of the kinetic Cucker-Smale flocking model with chemotactic movements (with C. Chen and S.-Y. Ha). submitted.
• Boundary effect in Lamb’s problem (with H. Wang and S. Yu). preprint.
• On the global well-posedness for the kinetic Winfree model in a large coupling strength regime (with D. Amadori, S.-Y Ha and J. Park). preprint.
• Uniform stability of Temperature Cucker Smale Model (with S.-Y. Ha, J. Kim, C. Min and T. Ruggeri). preprint.
• Relation between first and second order system and its applications (with S.-Y. Ha and J. Park). preprint.
• Flocking emergence of hydrodynamic Cucker-Smale model near vacuum (with S.- Y. Ha). preprint.
• Asymptotic alignment of particle and kinetic models with attractive-repulsive couplings (with S.-Y. Ha, K.-K. Kang, and J. Park). Preprint.