师资队伍
教授
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  • 姓名尧小华
  • 职称教授/博导
  • 办公室六号楼M510
  • 邮箱yaoxiaohua@mail.ccnu.edu.cn
个人简介 Brief Introduction
开设课程 Courses
研究方向 Research Interests 
调和分析与偏微分算子,研究兴趣主要集中在调和分析与偏微分方程的交叉领域;
具体包括如下几个主题:
1. 振荡积分与色散估计的研究;
2. 微分算子相关的调和分析问题的研究;
3. Schrödinger 算子的研究;
4. 数学物理相关问题的研究
教育经历 Education Experience
1994.9-1998.6 华中理工大学数学系本科,并获应用数学学士学位;
1998.9-2001.6 华中科技大学数学系硕士,并获应用数学硕士学位;
2001.9-2004.6 兰州大学数学系博士,并获基础数学博士学位。
工作经历 Work Experience
1998.7-2003.7 华中科技大学数学系任助教;
2003.7-2003.10 华中科技大学数学系任讲师;
2003.10-2009.7 华中师范大学大学任副教授
2009.7- 华中师范大学大学任教授
2011.7- 华中师范大学大学任博士生导师
2004.2-2004.5 美国新泽西Rutgers大学数学系访问;
2008.2-2008.7 北京师范大学数学学院访问,
2009.8-2009.11 中科院应用物理与计算数学研究所客座访问,
2011.3-2012.3 美国Johns Hopkins University 高级访问学者,
2011.3 入选2010年教育部新世纪优秀人才计划,
2013.9-2013.10 澳大利亚Macquarie大学数学系访问,
2014.1-2014.2 美国普林斯顿高等研究所访问
研究成果 Research Results
主要论著目录: (论文PDF可在researchgate网站找到)
https://www.researchgate.net/profile/Xiaohua_Yao/contributions
26. Liejun Shen, Xiaohua Yao, Least energy solutions for a class of fractional Schrödinger-Poisson systems, Journal of Mathematical Physics 59, 081501 (2018);
25. E. S.Selima, X.Yao, A.M. Wazwaz, Multiple and exact soliton solutions of the perturbed KdV equation of long surface waves in a convective fluid via Painlevé analysis, factorizationand simplest equation methods, Physical Review E 95, 062211 (2017).
24. C.Sun,H. Wang, X.Yao, J.Zheng, Scattering Below Ground State of Focusing Fractional Nonlinear Schrodinger Equation with Radial Data, To appear in Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 2018,38(4): 2207-2228
23. Q. Deng, Y. Ding, X. Yao, Riesz transforms associated with higher order Schrodinger typeoperators, Potential Analysis, 2018, 49(3): 381-410.
22. H.Feng, A. Soffer and X. Yao, Decay Estimates and Strichartz Estimates of the Fourth-order Schrodinger Operator, J. Functional Analysis, 274(2018),605-658.
21. Q. Deng, A. Soffer and X. Yao, Soliton-potential interactions for nonlinear Schrodinger equation in R3, Siam J. in Math. Anal., 2018, 50(5): 5243-5292
20. S. Huang, X. Yao, Q. Zheng, Remarks on the Lp-limiting sbsorption principle of Schrodinger operator and applicaions to spectral multipliers, Forum Math. 2018,30(1): 43-55
19. Q. Deng, A.Soffer, X. Yao, Endpoint Strichartz Estimates for Charge Transfer Hamiltonians, Indiana Univ. Math. J. 2018,67: 2487-2522
18. A. Sikora, L. Yan, X. Yao, Spectral multipliers, Bochner-Riesz means and uniform Sobolev inequalities for elliptic operators. International Mathematics Research Notices(IMRN),2018(10): 3073-3121
17. E.S.Selima , A. R. Seadawy, X. Yao, The nonlinear dispersive Davey-Stewartson system for surface waves propagation in shallow water and its stability,European Physical Journal Plus131(12), 2016
16. Q. Deng, Y. Ding, X. Yao, Lq estimates of Riesz transforms associated to Schrodinger operators, J. Aust. Math. Soc. 101 (2016), 290–309
15. J.Bourgain, P. Shao, C. Sogge, X.Yao, On L^p-resolvent estimates and the density of eigenvalues for compact Riemannia manifolds . Communications in Mathematical Physics, 333(2015), 1483-1527
14. Deng Q, Ding Y, Yao, X., Maximal and minimal forms for generalized Schrodinger operator , Indiana Univ. Math. J. 63 (2014), 727-738
13. Deng Q, Ding Y, Yao,X., The pointwise estimates of heat kernel of higher order Schrodinger type semigroups. J. Functional Analysis, 266(2014), 5377–5397.
12. A. Sikora, Linxin Yan,Xiaohua Yao, On the boundedness of spectral multipliers for operators with generalized Gaussian estimates, J. Functional Analysis, 266 (2014), 368–409
11. Peng Shao, Xiaohua Yao, Uniform Sobolev resolvent estimates for Laplace-Beltrami operators on compact manifolds. International Mathematics Research Notices.(IMRN), Vol. 2014, No. 12, pp. 3439–3463.
10. Chao Deng, Xiaohua Yao, Well-posedness and ill-posedness of 3D-incompressible generalized Navier-Stokes equations in Triebel-Lizorkin spaces, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), V. 34, No. 2, 2014
9. Deng Q, Ding Y, Yao, X., Hardy spaces associated with higher-order divergence eilliptic operator. J. Functional Analysis,263(2012), 604-674
8. Chen W, Miao C, Yao X., Dispersive estimates with geometry of finite type. Communication in Partial Differential Equations. 37: 479–510, 2012
7. Kim J., Arnold, A. Yao X. , Global estimates of fundamental solutions for higher-order Schrödinger equations. Monatshefte für Mathematik, 168 (2012), 253-266
6. Zheng Q., Yao X., Higher-Order Kato Class Potentials for Schrödinger operators. Bulletin of London Math. Soc., 41(2009), 293-301.
5. Ding Y., Yao X., Lp-Lq Estimates for dispersive Equations and related applications. J. Math. Anal. Appl., 356( 2009), 711-728.
4. Ding Y., Yao X., Hp-Hq Estimates for dispersive Equations and related applications. J. Functional Analysis , 257 (2009) 2067–2087
3. Yao X., Zheng Q., Oscillatory integrals and Lp Estimates for Schrödinger Equations. Journal of Differential Equation, 244(2008), 741-752.
2. Zheng Q., Li L., Yao X., and Fan D., The Spectrum of differential operators in Hp spaces. Illinois Journal of Math. 49(2005),45-621.
1. Zheng Q., Yao X. and Fan D., Convex hypersurfaces and Lp estimates for Schrödinger equations. J.Functional Ananlysis, 208(2004), 122-139.
研究项目 Research Projects
1. 国家数学天元基金项目(No. 10726023) 振荡积分与高阶Schrödinger方程解的Lp估计, 3万元, 2008.1-2008.12.
2. 国家数学青年基金项目(No. 10801057) 调和分析在Schrödinger方程解的Lp估计中的应用,17万元, 2009.1-2011.12.
3. 教育部重点项目(No. 109117) 在Hp和Lp中微分算子的若干研究,10万元,2009.1-2011.12.
4. 中央高校基本科研业务费(No. CCNU09A02015, 高阶波;动方程的若干研究,10万元,2009.1-2011.12.
5. 新世纪优秀人才计划项目, 50万元, 2011.1-2013.12.
6. 国家自然科学面上基金(No. 11371158) 调和分析对色散估计及谱理论的应用, 62万元, 2014.1-2017.12
7. 参与教育部长江学者创新团队计划建设,2014-2016.
8. 国家自然科学面上基金(No.11771165) 调和分析对微分算子应用的研究,48万元直接经费,2018.1-2021.12.
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