2016年1月—2020年12月, 国家自然科学基金重点项目（1531006）,随机动力系统的有效动力学及其刻画, 主持人,直接经费230万.

2018年1月—2021年12月，国家自然科学基金，随机偏微分方程解的适定性与正则性及相关问题研究(11771123)，参与，48万.

2022年1月—2025年12月,国家自然科学基金项目（12171084）， 非马尔可夫噪声驱动的随机偏微分方程的动力学，主持人， 51万.

Selected Publications

1. H. Gao and J. E. M. Rivera, Global existence and decay for thesemilinear thermoelastic contact problem, J. Differ. Eqns., Vol 186(2002), 52--68.

2. H. Gao and C. Bu, Dirichlet inhomogeneousboundary value problem for the n+1 complex Ginzburg-Landau equation,  J.Differ. Eqns. 198(2004), 176--195.  

3. C. Sun, H. Gao, J. Duanand B. Schmalfuss, Rare Events in the Boussinesq System with Fluctuating Dynamical BoundaryConditions,  J. Differ. Eqns., 248 (2010), no. 6, 1269–1296. 

4.  F.Guo, H. Gao and Y. Liu, Existence of permanent andbreaking waves for the periodic Degasperis- Procesi equation with lineardispersion, Journal für reine und angewandteMathematik, Volume 2011, Issue 657, Pages 199–223.

5. Y.Chen, H. Gao and B. Guo, Well posedness for stochastic Camassa-Holmequation, J. Differ. Eqns., 253( 2012),  2353–2379. 

6. F. Guo, H. Gao and Y. Liu, On the wave-breakingphenomena for the two-component Dullin-Gottwald-Holmsystem, J. Lond. Math. Soc. (2), 86(2012), no. 3, 810–834. 

7. H. Gao, F. Liang and B. Guo, Stochastic wave equations with nonlinear damping and source terms, Infinite Dimensional Analysis, QuantumProbability and Related Topics, 16 (2013), no. 2, 1350013, 29 pp.   

8. Y. Han, F. Guo and H. Gao, On solitary waves and wave-breaking phenomena fora generalized two-component integrable Dullin-Gottwald-Holm system, J. Nonlinear Sci., 23 (2013), no.4, 617–656.

9. H. Gao,M. J. Garrido-Atienza and B. Schmalfuss, Random attractors for stochasticevolution equations driven by fractional Brownian motion, SIAM J. Math. Anal., 46 (2014), no. 4, 2281–2309.

10. J. Fan, H. Gao and B. Guo, Uniqueness of Weak Solutions to the 3DGinzburg– LandauSuperconductivity Model,  International Mathematics Research Notices, 2015(2015), 1239-12.  

11. Y. Chen and H.Gao, The Cauchy problem for the Hartree equations under random influences, J. Differ. Eqns.,  259(2015), 5192-5219.

12. L. Fan, H. Gao and Y. Liu, On the rotation-two-component Camassa-Holm system modelling the equatorialwater waves, Advances in Mathematics, 291(2016), 59–89.   

13.Y. Chen and H. Gao, Well-posedness and Large Deviations of theStochastic Modified Camassa-Holm Equation,Potential Analysis，45 (2016), 331–354.  

14.L. Fan and H. Gao, Instabilityof equatorial edge waves in the background flow,  Proceedings of the AMS，145 (2017), 765–778.  

15. Y. Chen and H. Gao, Well-posedness and large deviations for a classof SPDEs with Levy noise, J. Differ. Eqns.,  263(2017), 5216-5252.

16 .M. Chen, L. Fan, H. Gao ang Y. Liu, Breaking waves andsolitary waves to the Rotation-Two- Component Camassa-Holm System, SIAM J. Math.  Anal., 49(2017),3573-3602.

17. Lin Lin and H. Gao, A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise, J. Theoretical Probab., 32(2019), 460–483.

18. G. Lv, H.Gao, J. Wei and J. Wu, BMO and Morrey-Campanatoestimates for stochastic convolutions and Schauder estimates for stochasticparabolic equations, J. Differ. Eqns., 266(2019), 2666–2717. 

19. H. Gao and H. Liu, Well-posednessand invariant measures for a class of stochastic 3D Navier-Stokes equationswith damping driven by jump noise, J. Differ. Eqns., 267 (2019), 5938–5975.

20. J. Wei, J. Duan, H. Gao and G. Lv, Stochastic strong solution for stochastic transport equations, Stochastics and Partial DifferentialEquations: Analysis and Computations，9 (2021), no. 1, 105–141.

21. H. Gao, M. J. Garrido-Atienza, A. Gu, K. Lu andB. Schmalfuss, Rough path theory to approximate random dynamical systems, SIAM J. Appl. Dynamical Sys.,20 (2021),  997–1021.

22. B. Wang and H. Gao, Exponential stability ofsolutions to stochastic differential equations driven by G-Levy process, Appl. Math. Optim.,83 (2021), 1191–1218.

23. Y. Chen, J. Duan and H. Gao, Wave-breaking and moderate deviationsof the stochastic Camassa-Holm with pure jump noise, Physica D,  424 (2021), PaperNo. 132944, 12 pp.

24. H. Gao and Y. Shi,Averaging principle for a stochastic coupled fast-slow atmosphere-ocean model, J. Differ. Eqns., 298 (2021), 248–297.