Yang Jianwei Job Title: Special Associate Researcher E-mail: jw-urbain.yang@bit.edu.cn
After receiving his PhD in 2015, he did postdoctoral research in Peking University and the Thirteenth University of Paris, France, focusing on some fundamental problems in analysis and the long-term dynamic qualitative theory of solutions to nonlinear dispersion equations. 2019 International Visiting Scholar sponsored by LabexMME-DII, France. Since the spring of 2020, I have been teaching the real variable function course of Mathematics and statistics. In the following year, I began to take on the teaching task of linear Algebra B. He won the third prize of the Young teachers' teaching competition. He was awarded the project of National Natural Science Foundation of China (NSFC). The project name is: Long-term dynamical properties of initial boundary value problems in the Outer Region of nonlinear wave equations.
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Analysis and partial differential equations. This paper mainly deals with the long-term dynamic qualitative theory of solutions of nonlinear dispersive partial differential equations and the harmonic analysis problems related to dispersion equations. At present, he focuses on the long time dynamic classification of nonlinear wave equations based on soliton solutions, harmonic analysis related to Fourier constraint theorem and so on.
September 2012 -- June 2015, Doctor of Basic Mathematics, China Academy of Engineering Physics, Supervisor, Miao Changxing
September 2009 -- June 2012, Master of Basic Mathematics, China Academy of Engineering Physics, Supervisor, Miao Changxing
September 2005 -- July 2009, Mathematics and Applied Mathematics, Bachelor degree, School of Mathematical Sciences, Nankai University
July 2018 - Present, Beijing Institute of Technology, Special Associate Researcher
July 2015 - June 2018, Beijing International Center for Mathematical Research, Postdoctoral Fellow, Co-supervisor, Gang Tian
From January 2016 to January 2017, Postdoctoral Fellow, Co-Supervisor Thomas Duyckaerts, Universitat Paris XIII
December 2018 - November 2019, Visiting Scholar, Labex MME-DII Exchange Program, University of Paris Nord
[1] Yang, J. Sharp null form estimates on endline geometric conditions of the cone, preprint, arXiv:2208.02911
[2] Yang, J. An endline bilinear restriction estimate for paraboloids, arXiv:2202.13905
[3] Duyckaerts, T. and Yang, J: Scattering to a stationary solution for the super-quintic radial wave equation outside an obstacle. Ann. Inst. Fourier (Grenoble) 71 (2021), no. 5, 1845–1884.
[4] Duyckaerts, T. and Yang, J: Blow-up of a critical Sobolev norm for energy-subcritical and energy-supercritical wave equations. Analysis and PDE. Vol. 11 (2018), no. 4, 983-1028.
[5] C. Miao, G. Xu, J. Yang: Global well-posedness for the defocusing Hartree equation with radial data in R4. Commun. Contemp. Math. Vol.22 (2020), no. 2, 1950004, 35pp
[6] C. Miao, C. D. Sogge, Y. Xi, J. Yang: Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces. Journal of Functional Analysis, 271 (2016), no. 10, 2752-2775.
[7] Yang, J.: Nonlinear Schrödinger equations on compact Zoll manifolds with odd growth. Sci. China Math. 58 (2015), no. 5, 1023-1046.
[8] C. Gao, C. Miao, J. Yang: The inter-critical defocusing nonlinear Schrödinger equations with radial initial data in dimensions four and higher. Anal. Theory. Appl. Vol. 35 (2019), no. 2. 205-234.
[9] G. Xu, and J. Yang: Long time dynamics of the 3D radial NLS with the combined terms. Acta. Math. Sin. (Engl. Ser.) Vol. 32 (2016), no. 5, 521-540.
[10] C. Miao, J. Yang, J. Zheng: On local smoothing problems and Stein's maximal spherical means. Proceedings of the American Mathematical Society. 145 (2017), no. 10, 4269-4282.
[11] C. Miao, J. Yang, T. Zhao: The global well-posedness and scattering for the 5-dimensional defocusing conformal invariant NLW with radial initial data in a critical Besov space. Pacific J. Math. Vol. 305 (2020), no. 1, 251-290.
[12] C. Miao, J. Yang, J. Zheng: An improved maximal inequality for 2D fractional order Schrödinger operators, Studia Math. 230 (2015), no. 2, 121-165.
[13] C. Miao, J. Yang, J. Zheng: On Wolff’s L5/2−Kakeya maximal inequality in R3, Forum Math. 27 (2015), no. 5, 3053-3077
[14] C. Gao, C. Miao, J. Yang: Square function inequality for a class of Fourier integral operators satisfying cinematic curvature conditions. Forum Math. 32(2020), no. 6, 1375-1394.
[15] C. Miao and J. Yang: Oscillatory integrals involving the Carleson–Sjölin conditions and several applications, Methods and Applications of Analysis 28 (4) 2021:467-486. DOI:10.4310/MAA. 2021. v28.n4.a4
[16] J. Yang: Global existence for nonlinear system of wave equations in 3-D domains. Appl. Math. (Warsaw) 38 (2011), no. 4, 435-452
[17] Thomas DUYCKAERTS AND Jianwei YANG, Dispersive estimates for wave and Schrödinger equations with a potential in non-trapping exterior domains , arXiv:2401.12608
[18] Thomas DUYCKAERTS AND Jianwei YANG, Center stable manifolds for the radial semi-linear wave equation outside a ball, arXiv:2401.12581