معرفی
Xinliang An is an Associate Professor of Mathematics at the National University of Singapore (NUS), where he joined in July 2018. His research focuses on understanding singularity formation, regularity, asymptotic stability, long time behavior, and geometric shapes of solutions to important partial differential equations, with particular emphasis on Einstein's equations in general relativity, Euler equations and Navier-Stokes equations in fluid dynamics, and elastic wave equations in elastic mechanics.
Dr. An received his Ph.D. in June 2014 from the Department of Mathematics at Princeton University, where he was advised by Professor Sergiu Klainerman, a renowned expert in general relativity and partial differential equations. His doctoral work laid the foundation for his subsequent research on gravitational collapse and singularity formation.
Dr. An's research spans multiple areas of mathematical physics, with a focus on gravitational collapse, big bang singularities in cosmology, and the detailed mathematical analysis of fluid dynamics and elastic mechanics. His work bridges pure mathematics with theoretical physics, particularly in understanding the formation of singularities in Einstein's equations. He has made significant contributions to the mathematical theory of black hole formation, including the emergence of apparent horizons and the analysis of spacelike singularities inside black holes. His recent work extends to studying the stability of Taylor-Couette flows in fluid dynamics, demonstrating how rotational effects influence dissipation rates through enhanced dissipation phenomena.
Analysis of Dr. An's publication record reveals a strong progression from vacuum spacetimes to more complex physical systems. His early work focused on trapped surface formation in vacuum Einstein equations, then expanded to include electromagnetic fields (Einstein-Maxwell system), charged scalar fields, and fluid dynamics. A key theme across his publications is the development of scale-critical techniques to analyze singularity formation, with numerous papers establishing polynomial blow-up upper bounds for various geometric quantities near singularities. His research demonstrates exceptional technical mastery in handling non-strictly hyperbolic systems with multiple wave speeds.
Dr. An has made significant methodological contributions by connecting Christodoulou's short-pulse method with Klainerman-Rodnianski's signature counting argument to the peeling properties studied in small-data regimes. This innovative approach has allowed him to avoid elliptic estimates and geometric renormalizations in some cases, providing new technical improvements and simplifications to existing results. His work on low-regularity ill-posedness for elastic wave systems has established that the Cauchy problem for 3D elastic waves is ill-posed in H³(ℝ³) due to instantaneous shock formation.
