Shih-Hsien Yu

Shih-Hsien Yu (born February 16, 1964) is a Taiwanese mathematician at the National University of Singapore (NUS). He is known for his work on hyperbolic conservation laws and kinetic equations.

Yu was born in Taiwan, and attended Taichung first senior high School. He did his undergraduate studies and master courses at National Taiwan University, followed by graduate studies at Stanford University, working under Tai-Ping Liu and obtaining his PhD in 1994. He was subsequently a postdoc fellow at University of Minnesota (1994–1995), faculty member at University of California, Los Angeles (1995–1999), Osaka University (1999–2000), City University of Hong Kong (2000–2007), before moving to the National University of Singapore in 2007.

With Tai-Ping Liu, Yu has solved several basic problems in conservation laws and kinetic equations such as the existence of discrete shock wave for Lax-Friedrichs scheme, and the positive-valued function property of the Boltzmann shock profile, pointwise structure of the Green’s functions for linearized Boltzmann equation, and invariant manifolds for stationary Boltzmann flows.

1. Continuum shock profiles for discrete conservation laws. I. Construction (with Tai-Ping Liu), Comm. Pure Appl. Math. 52 (1999) no. 1, 85–127.
2. Boltzmann equation: micro-macro decompositions and positivity of shock profiles (with Tai-Ping Liu), Comm. Math. Phys. 246 (2004), no. 1, 133–179.
3. The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation (with Tai-Ping Liu), Comm. Pure Appl. Math. 57 (2004), no. 12, 1543–1608
4. Nonlinear wave propagations over a Boltzmann shock profile, J. Amer. Math. Soc. 23 (2010), no. 4, 1041–1118.
5. Invariant manifolds for steady Boltzmann flows and applications (with Tai-Ping Liu), Arch. Ration. Mech. Anal. 209 (2013), no. 3, 869–997.

Yu was an invited speaker at the International Congress of Mathematicians(ICM) in 2014 (Partial Differential Equations section).