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李梦妮
副教授
数学学院
应用数学系
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lmn@seu.edu.cn
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  • 基本信息
  • 研究成果
  • 项目与荣誉
  • 社会兼职
  • 李梦妮，清华大学博士，东南大学副教授。主要从事几何分析和偏微分方程领域的理论研究，已在非线性波动方程、流体力学方程以及完全非线性椭圆方程等方面发表多篇论文，部分代表性成果发表于Adv. Math. (2023独立), Ann. Mat. Pura Appl. (2025), JDE (2021, 2025)等期刊。主持国家自然科学基金青年C类项目(2023-2025)与江苏省自然科学基金青年项目(2022-2025)。受邀在第九届世界华人数学家大会(ICCM 2022)作45分钟邀请报告，受推荐在中国数学会2024年学术年会作偏微分方程分组分组报告。指导学生获2025年东南大学校庆研究生学术报告会优秀论文。
    2025-至今 东南大学 副教授 Associate Professor, Southeast University. 2022-2024 东南大学 讲师 Lecturer, Southeast University. 2017-2022 清华大学 博士 Ph. D., Tsinghua University. 2013-2017 中山大学 学士 B.S., Sun Yat-sen University.
    Mengni Li received her Ph.D. from Tsinghua University and is now an associate professor at Southeast University. Her research interests include nonlinear partial differential equations (PDEs) related to wave phenomena, fluid dynamics, and affine geometry, with a particular emphasis on wave equations, magnetohydrodynamics (MHD) equations, and Monge-Ampère type equations. She is passionate about developing existing topics as well as exploring new ones. Among her independent contributions, she constructed an inverse scattering theorem for one-dimensional semi-linear wave equations with null structure, published in the Journal of Hyperbolic Differential Equations, and as a follow-up, she further developed an inverse scattering theory for nonlinear Alfvén waves in ideal incompressible MHD, published in Advances in Mathematics.

  • [MR4191506] Li, Mengni. Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions. Communications on Pure and Applied Analysis. Vol. 20, No. 1, pp. 301-317, 01, 2021.

    [MR4223342] Li, Mengni; Yu, Pin. On the rigidity from infinity for nonlinear Alfvén waves. Journal of Differential Equations. Vol. 283, pp. 163-215, 05, 2021.

    [MR4248705] Li, Mengni. An inverse scattering theorem for (1+1)-dimensional semi-linear wave equations with null conditions. Journal of Hyperbolic Differential Equations. Vol. 18, No. 1, pp. 143-167, 04, 2021.

    [MR4258125] Li, Mengni. Asymptotic behavior of global solutions to one-dimension quasilinear wave equations. Dynamics of Partial Differential Equations. Vol. 18, No. 2, pp. 81-100, 05, 2021.

    [MR4331266] Li, Mengni. Singular Monge-Ampère equations over convex domains. Electronic Journal of Differential Equations. Vol. 2021, Paper No. 86, pp. 1-18, 10, 2021.

    [MR4350513] Li, You; Li, Mengni. Boundary Hölder regularity for a class of fully nonlinear elliptic partial differential equations. Nonlinear Analysis. Theory, Methods & Applications. Vol. 216, Paper No. 112681, pp. 1-19, 03, 2022.

    [MR4375859] Li, Mengni; Li, You. Global regularity for a class of Monge-Ampère type equations. Science China. Mathematics. Vol. 65, No. 3, pp. 501-516, 03, 2022.

    [MR4446898] Li, Mengni. Global existence and scattering behavior for one dimensional wave maps into Riemannian manifolds. Results in Mathematics. Vol. 77, No. 4, Paper No.164, pp. 1-26, 08, 2022.

    [MR4550205] Ji, Jingwen; Jiang, Feida*; Li, Mengni. Entire subsolutions of a kind of k-Hessian type equations with gradient terms. Communications on Pure and Applied Analysis. Vol. 22, No. 3, pp. 946-969, 03, 2023.

    [MR4610304] Li, Mengni; Li, You*. Boundary lower estimates for a class of fully nonlinear elliptic partial differential equations. Frontiers of Mathematics (Hosted by Peking University). Vol. 18, No. 1, pp. 81-104, 01, 2023.

    [MR4658830] Li, Mengni. Inverse scattering of Alfvén waves in three dimensional ideal magnetohydrodynamics. Advances in Mathematics. Vol. 435, Paper No. 109363, pp. 1-69, 12, 2023.

    [MR4675093] Li, You; Li, Meng Ni; Liu, Yan Nan. Boundary regularity for k-Hessian equations. Acta Mathematica Sinica (English Series). Vol. 39, No. 12, pp. 2393-2413, 12, 2023.

    [MR4684533] Li, Mengni. Unilateral rigidity from infinity for nonlinear Alfvén waves in ideal magnetohydrodynamics. Discrete and Continuous Dynamical Systems. Series B. Vol. 29, No. 2, pp. 760-776, 02, 2024.

    [MR4756932] Li, Mengni; Wang, Yan-Lin*. Zero-viscosity limit for Boussinesq equations with vertical viscosity and Navier boundary in the half plane. Nonlinear Analysis. Real World Applications. Vol. 80, Paper No.104150, pp. 1-16, 12, 2024.

    [MR4798887] Li, Mengni; Li, You*. Existence, uniqueness and interior regularity of viscosity solutions for a class of Monge-Ampère type equations. Journal of Differential Equations. Vol. 415, pp. 202-234, 01, 2025.

    [MR4883222] Jiang, Feida; Ji, Jingwen*; Li, Mengni. Necessary and sufficient conditions on entire solvability for real (n-1) Monge-Ampère equation. Annali di Matematica Pura ed Applicata (1923 -). Vol. 204, No. 2, pp. 447-476, 04, 2025.