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尧小华

English Version (英文版)

职称教授/博导
办公室六号楼M510
邮箱yaoxiaohua@ccnu.edu.cn

个人简介

华中师范大学数学与统计学院教授、博士生导师，2010年入选教育部新世纪人才计划；作过高级访问学者曾在美国Johns Hopkins大学留学一年。目前主要从事调和分析与微分算子的研究；在色散方程、微分算子及函数空间等方向上开展研究工作；主要学术成果发表在 “Adv.in Math.”“Comm. Math. Phys.”、 “Trans. AMS”、 “Inter. Math. Res. Notices”、“J. Functional Analysis”、“Comm. Partial Differential equation”、“Siam J. Math. Anal.” “Siam J. Appl. Math.”等国际重要数学期刊上；连续主持多项国家自然科学基金面上项目，也曾主持过教育部科学技术研究重点项目及新世纪优秀人才计划等多个科研项目；作为核心成员参与了华中师范大学教育部创新团队（偏微分方程）建设。

开设课程

实变函数，泛函分析，Fourier分析（本科生课程）
调和分析，偏微分算子分析，薛定谔算子，振荡积分，非线性色散方程（研究生课程）

研究方向

Fourier分析及其应用，微分算子谱理论与偏微分方程

教育经历

1994.9-1998.6  华中理工大学应用数学系本科
1998.9-2001.6  华中科技大学应用数学系硕士
2001.9-2004.6  兰州大学基础数学系博士

工作经历

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
2017.7-2017.8     澳大利亚Monash大学数学系访问
2018.12-2019.1    台湾中央大学数学系访问

研究成果

36、Haruya Mizutani, Zijun Wan, and Xiaohua Yao, Lp-boundedness of wave operators for bi-Schrödinger operators on the line. Advances in Mathematics, 451(2024), 109806. 
35、Li, Peijun; Yao, Xiaohua; Zhao, Yue，The Scattering Resonances for Schrödinger-Type Operators with Unbounded Potentials，SIAM J. Math. Anal. 56 (2024), no. 2, 2149–2170.
34、Yao, Xiaohua; Zhao, Yue， Stability for an inverse spectral problem of the biharmonic Schrödinger operator，J. Differential Equations 377 (2023), 694–711.
33、 Li, Ping; Soffer, Avy; Yao, Xiaohua，Decay estimates for fourth-order Schrödinger operators in dimension two，J. Funct. Anal. 284 (2023), no. 6, Paper No. 109816, 83 pp.
32、Avy Soffer, Zhao Wu and Xiaohua Yao, Decay estimates for bi-Schrodinger operators in dimension one, Ann. Henri Poincaré 23 (2022), no. 8, 2683-2744.
31、Li, Peijun; Yao, Xiaohua; Zhao, Yue Stability of an inverse source problem for  biharmonic operators, SIAM J. Appl. Math. 81-6 (2021), pp. 2503-2525
30、Haruya Mizutani, XiaohuaYao, Kato smoothing, Strichartz and uniform Sobolev estimates for fractional operators with sharp Hardy potentials, Communications in Mathematical Physics, 388(2021), 581-623.
29、Qing Guo, Hua Wang, Xiaohua Yao, Dynamics of the focusing 3D cubic NLS with slowly decaying potential, J. Math. Anal. Appl., Vol. 506, No. 2(2022), 1-30.
28、Li, Peijun; Yao, Xiaohua; Zhao, Yue， Stability of an inverse source problem for the damped biharmonic plate equation. Inverse Problems 37 (2021), no. 8, No. 085003, 19 pp
27．Deng, Qingquan; Yao, Xiaohua Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations with time-dependent potential. J. Math. Phys. 61 (2020), no. 4, 041504, 35 pp.
26. Feng, Hongliang; Soffer, Avy; Wu, Zhao; Yao, Xiaohua; Decay estimates for higher-order elliptic operators. Trans. Amer. Math. Soc. 373 (2020), no. 4, 2805–2859. 
25. Deng, Qingquan; Ding, Yong; Yao, Xiaohua Riesz transforms associated with higher-order Schrödinger type operators. Potential Anal. 49 (2018), no. 3, 381–410. 
24. Shen, Liejun; Yao, Xiaohua Least energy solutions for a class of fractional Schrödinger-Poisson systems. J. Math. Phys. 59 (2018), no. 8, 081501, 21 pp.
23. Sun, Chenmin; Wang, Hua; Yao, Xiaohua; Zheng, Jiqiang Scattering below ground state of focusing fractional nonlinear Schrödinger equation with radial data. Discrete Contin. Dyn. Syst. 38 (2018), no. 4, 2207–2228. 
22. A. Sikora, L. Yan, X. Yao*, Spectral multipliers, Bochner-Riesz means and uniform Sobolev inequalities for elliptic operators, Inter. Math. Res. Notices (IMRN), (10)2018, 3070-3121.
21. Q. Deng, A. Soffer, X. Yao*, Soliton-potential interactions for nonlinear Schrödinger equations in R^3, Siam J. Math. Anal., 50(2018), 5243-5292.
20. Huang, Shanlin; Yao, Xiaohua; Zheng, Quan Remarks on $L^p$-limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems. Forum Math. 30 (2018), no. 1, 43–55.
19. H. Feng, A. Soffer, X. Yao*, Decay estimates and Strichartz estimates of fourth-order Schrödinger operator, J. Funct. Analysis, 274(2018), 605-658.
18. Q. Deng, A. Soffer, X. Yao*, Endpoint Strichartz Estimates for Charge Transfer Hamiltonians, Indiana Univ. Math. J., (67) 2018, 2487-2522
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  Riemannian 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 elliptic 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 Analysis, 208(2004), 122-139.

研究项目

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、教育部科学研究重点项目（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、教育部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、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，2018.1-2021.12.
8、国家自然科学面上基金（No.12171182）
调和分析在微分算子若干研究中的应用，51万元，2022.1-2025.12.

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