Research:

Nonlinear mechanics
Fluid mechanics
Nonlinear waves
Turbulence
Chaos
Analytical approximation method
Numerical calculation method
Three-body problem

Selected Publications: 

1. S.J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall\CRC Press, Boca Raton, 2003.

2. S.J. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, Springer & Higher Education Press, Heidelberg & Beijing, 2012.

3. X.Y. Yang, F. Dias and S.J. Liao, “On the steady-state resonant acoustic gravity wave”, J. Fluid Mech., vol. 849, pp. 111-135 （2018）

4. X.X. Zhong and S.J. Liao, “On the limiting Stokes’ wave of extreme height in arbitrary water depth”, J. Fluid Mech., vol. 843, pp. 653-679 (2018).

5. Z. Liu, D.L. Xu and S.J. Liao, “Finite amplitude steady-state wave groups with multiple near resonances in deep water”, J. Fluid Mech., vol. 835, pp. 624-653 (2018) (DOI: doi.org/10.1063/1.5004452)

6. S.J. Liao, D.L. Xu and M. Stiassnie, “On the steady-state nearly resonant water waves”, Journal of Fluid Mechanics, vol. 794, pp. 175-199 (2016) (DOI: 10.1017/jfm.2016.162).

7. Z. Liu, D.L. Xu, J. Li, T. Peng, A. Alsaedi and S.J. Liao, “On the existence of steady-state resonant waves in experiment”, Journal of Fluid Mechanics, vol. 763, pp. 1-23 (2015) (DOI: 10.1017/jfm.2014.658).

8. Z. Liu and S.J. Liao, “Steady-state resonance of multiple wave interactions in deep water”, Journal of Fluid Mechanics, vol. 742, pp. 664-700 (2014) (DOI: 10.1017/jfm.2014.2).

9. D.L. Xu, Z.L. Lin, S.J. Liao and M. Stiassnie, “On the steady-state fully resonant progressive waves in water of finite depth”, Journal of Fluid Mechanics, vol. 710, pp. 379-418 (2012) (DOI: 10.1017/jfm.2012.370).

10. S.J. Liao, “On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet”, Journal of Fluid Mechanics, vol. 488, pp. 189-212 (2003) (DOI: 10.1017/S0022112003004865).

11. S.J. Liao and A. Campo, “Analytic solutions of the temperature distribution in Blasius viscous flow problems”, Journal of Fluid Mechanics, vol. 453, pp. 411-425 (2002) (DOI: 10.1017/S0022112001007169).

12. S.J. Liao, “A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate”, Journal of Fluid Mechanics, vol. 385, pp. 101-128 (1999) (DOI: 10.1017/S0022112099004292).

13. Xiaochen Li, Xiaoming Li and Shijun Liao, “Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally”, Physics of Fluid, vol. 30, 012108 (2018)(DOI: 10.1063/1.5004452)

14. Jing Li, Xiaochen Li, Kaijie Chen, Bin Xie and Shijun Liao, “Faraday waves in a Hele-Shaw cell”, Physics of Fluid, vol. 30, 042106 (2018) (DOI: doi.org/10.1063/1.5022424)

15. Z. Liu, D.L. Xu and S.J. Lao, “Mass, momentum, and energy flux conservation between linear and nonlinear steady-state wave groups”, Physics of Fluid, Vol. 29, 127104 (2017)

16. H. Xu, Z.L. Lin, S.J. Liao, J.Z. Wu and J. Majdalani, “Homotopy based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls”, Physics of Fluids, vol. 22, 053601 (2010) (DOI: 10.1063/1.3392770).

17. S.J. Liao, “On the homotopy analysis method for nonlinear problems”, Applied Mathematics and Computation, vol. 147, pp. 499-513 (2004) (DOI: 10.1016/S0096-3003(02)00790-7).

18. S.J. Liao, “Notes on the homotopy analysis method: some definitions and theorems”, Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 983-997 (2009) (DOI: 10.1016/j.cnsns.2008.04.013).

19. S.J. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations”, Communications in Nonlinear Science and Numerical Simulation, vol. 15, pp. 2003-2016 (2010) (DOI: 10.1016/j.cnsns.2009.09.002).

20. X.M. Li and S.J. Liao, “Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems”, Applied Mathematics and Mechanics (English Edition), Vol. 39 (11), pp. 1529-1546. ( https://doi.org/10.1007/s10483-018-2383-6" target="_blank" rel="nofollow noopener noreferrer">https://doi.org/10.1007/s10483-018-2383-6 )

21. X.M. Li, Y.P. Jing and S.J. Liao, “Over a thousand new periodic orbits of planar three-body system with unequal mass”, Publications of Astronomical Society of Japan, 70 (4), 64 (1–7) (2018) (doi: 10.1093/pasj/psy057)

22. X.M. Li and S.J. Liao, “More than six hundred new families of Newtonian periodic planar collisionless three-body orbits”, Science China - Physics Mechanics & Astronomy, Vol. 60, No. 12, 129511 (2017) (doi: 10.1007/s11433-017-9078-5)

23. Z.L. Lin, L.P. Wang and S.J. Liao, “On the origin of intrinsic randomness of Rayleigh-Benard turbulence”, Science China - Physics Mechanics & Astronomy, vol. 60, No.1, 14712 (2017) (doi:10.1007/s11433-016-0401-5)

24. S.J. Liao, “Physical limit of prediction for chaotic motion of three-body problem”, Communications of Nonlinear Science and Numerical Simulations, vol. 19, pp. 601-616 (2014) (DOI: 10.1016/j.cnsns.2013.07.008).

25. S.J. Liao, “On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems”, Chaos, Solitons & Fractals, vol. 47, pp. 1-12 (2013) (DOI: 10.1016/j.chaos.2012.11.009).