H. Liu and C. Sparber (2007)

Rigorous Derivation of the Hydrodynamical Equations for Rotating Superfluids, to appear in M3AS.

H. Liu and Z.M. Wang (2007)
Superposition of multi-valued solutions in high frequency wave dynamics, to appear in Journal of Scientific Computing.

H. Liu and Z.M. Wang,
A field space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations
Journal of Computational Physics, 225 (2007), 591-614.

H. Liu and Z.M. Wang
Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations,
Applied Numerical Mathematics, 57 (2007), 821-836.

H. Liu, S. Osher and R. Tsai,

Multi-valued solution and level set methods in computational high frequency wave propagation, Commun. Comput. Phys. 1(5) (2006), 765-804.

S. Jin,  H.L. Liu, S. Osher and R. Tsai

Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, JCP, 210(2005), 498-518.

S. Jin,  H.L. Liu, S. Osher and R. Tsai

Computing multi-valued physical observables for the semiclassical limit of the Schroedinger equation, JCP, 205 (2005), 222-241.

H.T.  Fan and  H.L. Liu 
Pattern Formation, Wave Propagation and Stability in Conservation Laws  with  Slow Diffusion and Fast Reaction
 Journal of Hyperbolic Differential Equations, 1(4) (2004) 605--626.

 H.L. Liu, L.-T. Cheng and S. Osher (2003)
A level set framework for capturing  multi-valued solutions to nonlinear first-order equations, submitted.

 L.T. Cheng, H.L. Liu and S. Osher
Computational high frequency wave propagation using the level set method,  with applications to the semi-classical  limit of Schroedinger equations,  Comm. Math. Sci. Vol 1, No. 3 (2003), 593--621.

L.T. Cheng, H.L. Liu and S. Osher
High frequency wave propagation in Schroedinger equations using the Level Set method, preprint, 2003.