个人简介

江苏江阴人。现任William威廉William威廉教授。

研究兴趣

主要研究具有几何或物理背景的椭圆型偏微分方程，如Allen-Cahn方程、KP方程、Ginzburg-Landau方程等。

主讲课程

《复变函数论》，《数学分析》，《高等数学》等。

学习经历

1998年9月-2002年7月，四川大学数学系，本科；

2002年9月-2007年7月，北京大学数学科学学院，硕博连读。

工作经历

2007年7月-2018年10月，华北电力大学（北京）数理学院，讲师、副教授；

2008年9月-2011年9月，智利大学数学中心，博士后；

2018年11月-2024年9月，中国科学技术大学数学科学学院，教授；

2020年1月-2021年12月，中国科学院学部工作局，处长助理、副处长；

2024年9月至今，William威廉William威廉，教授。

主要科研项目

1. 国家自然科学基金面上项目，KP方程与Toda晶格相关问题的研究，2025，主持；

2. 国家自然科学基金面上项目，Gross-Pitaevskii方程及Ermakov系统相关问题的研究，2020，主持；

3. 国家自然科学基金青年项目，从Scherk曲面到Allen-Cahn方程的整体解， 2012，主持；

4. 科技部国家重点研发计划（子课题），Monge-Ampere方程，Allen-Cahn方程及极小曲面，2022，参与；

5. 国家自然科学基金专项项目，几何非线性椭圆偏微分方程，2022，参与；

6. 科技部国家重点研发计划（子课题）， 非线性偏微分方程及应用，2020，参与。

主要学术成果

Weiwei Ao, Yong Liu, Haicheng Yan, Wen Yang, Sharp estimates for bubbling solutions of an even order mean field equation, Communications in Contemporary Mathematics, accepted.

Y. Liu, Z. Wang, J. Wei, W. Yang, From KP-I lump solution to travelling waves of Gross-Pitaevskii equation, Journal de Mathématiques Pures et Appliquées 205 (2026) 103801.

Y. Liu, J. Wang, K. Wang, W. Yang, Y. Zhu, Existence and nonexistence of minimizer for Thomas-Fermi-Dirac-von Weizsacker model on lattice graph, Journal of Differential Equations, 438 (2025) 113360.

C. Li, Y. Liu, J. Wang, W. Yang, Existence of the fully nontrivial ground state solutions for the coupled nonlinear Brezis-Nirenberg Maxwell system, Journal of Differential Equations, 438 (2025) 113374.

L. Cai, Y. Liu, J. Wang, W. Yang, Existence and concentration phenomena along curves for the Schrodinger-Newton equation in R^3, Calculus of Variations and Partial Differential Equations, (2025) 64:189.

W. Liang, Y. Liu, J. Yang, From Toda lumps to singly periodic solutions of Allen-Cahn equation, J. Geometric Analysis 35 (2025) 84.

Y. Liu, J. Wei, W. Yang, Lump type solutions: Bäcklund transformation and spectral properties, Physica D: Nonlinear Phenomena 470 (2024) 134394.

W. Liang, Y. Liu, J. Yang, From Liouville equation to lump solutions of the 2+1 Toda lattice, Journal of Differential Equations 411 (2024) 478–505.

Y. Liu, Y. Zhang, Fence of saddle solutions of the Allen–Cahn equation in the plane, Proceedings of the Royal Society of Edinburgh: Section A Mathematics (2024) 1–42.

Y. Liu, J. Wei, W. Yang, Uniqueness of lump solution to the KP‐I equation, Proceedings of the London Math Soc 129 (2024) e12619.

L. Cui, Y. Liu, C. Wang, J. Wang, W. Yang, The Einstein-scalar field Lichnerowicz equations on graphs, Calculus of Variations and Partial Differential Equations 63 (2024) 138.

Y. Liu, K. Wang, J. Wei, K. Wu, On Dancer’s conjecture for stable solutions with sign-changing nonlinearity, Proc. Amer. Math. Soc. 152 (2024) 3485–3497.

Liu, Yong; Ma, Xi-Nan; Wei, Juncheng; Wu, Wangzhe, Entire solutions of the magnetic Ginzburg-Landau equation in R^4, The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 26(2)(2025), 757-811.

Liu, Yong; Tian, Jing; Yong, Xuelin, On the even solutions of the Toda system: a degree argument approach, Commun. Pure Appl. Anal. 21 (2022), no. 6, 1895–1916.

Liu, Yong; Wei, Juncheng, Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane, Rev. Mat. Iberoam. 38 (2022), no. 2, 355–432.

Ao, Weiwei; Liu, Yong; Wei, Juncheng, Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows, Phys. D 434 (2022), Paper No. 133258, 26 pp.

Liu, Yong; Wang, Kelei; Wei, Juncheng; Wu, Ke, Qualitative properties of stable solutions to some supercritical problems, Electron. Res. Arch. 30 (2022), no. 5, 1668–1690.

Ao, Weiwei; Huang, Yehui; Liu, Yong; Wei, Juncheng, Generalized Adler-Moser polynomials and multiple vortex rings for the Gross-Pitaevskii equation, SIAM J. Math. Anal. 53 (2021), no. 6, 6959–6992.

Liu, Yong; Wang, Kelei; Wei, Juncheng, On smooth solutions to one phase-free boundary problem in R^n, Int. Math. Res. Not. IMRN (2021), no. 20, 15682–15732.

Hamel, François; Liu, Yong; Sicbaldi, Pieralberto; Wang, Kelei; Wei, Juncheng, Half-space theorems for the Allen-Cahn equation and related problems, J. Reine Angew. Math. 770 (2021), 113–133.

Liu, Yong; Wei, Juncheng, Multivortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials, SIAM J. Math. Anal. 52 (2020), no. 4, 3546–3579.

Chen, Guoyuan; Liu, Yong; Wei, Juncheng, Nondegeneracy of harmonic maps from R^2 to S^2, Discrete Contin. Dyn. Syst. 40 (2020), no. 6, 3215–3233.

Yong, Xuelin; Li, Xiaoyu; Huang, Yehui; Ma, Wen-Xiu; Liu, Yong, Rational solutions and lump solutions to the (3+1)-dimensional Mel'nikov equation, Modern Phys. Lett. B 34 (2020), no. 3, 2050033, 14 pp.

Liu, Yong; Wei, Juncheng, Nondegeneracy, Morse index and orbital stability of the KP-I lump solution, Arch. Ration. Mech. Anal. 234 (2019), no. 3, 1335–1389.

Liu, Yong; Wei, Juncheng, On the Helmholtz equation and Dancer's-type entire solutions for nonlinear elliptic equations, Proc. Amer. Math. Soc. 147 (2019), no. 3, 1135–1148..

Liu, Yong; Wei, Juncheng, Nondegeneracy of the traveling lump solution to the 2+1 Toda lattice, J. Math. Phys. 59 (2018), no. 10, 101501, 26 pp.

Liu, Yong; Wang, Kelei; Wei, Juncheng, On a free boundary problem and minimal surfaces, Ann. Inst. H. Poincaré C Anal. Non Linéaire 35 (2018), no. 4, 993–1017.

Yong, Xuelin; Ma, Wen-Xiu; Huang, Yehui; Liu, Yong, Lump solutions to the Kadomtsev-Petviashvili I equation with a self-consistent source, Comput. Math. Appl. 75 (2018), no. 9, 3414–3419.

Liu, Yong; Wang, Kelei; Wei, Juncheng, Global minimizers of the Allen-Cahn equation in dimension n≥8, J. Math. Pures Appl. (9) 108 (2017), no. 6, 818–840.

Gui, Changfeng; Liu, Yong; Wei, Juncheng, Two-end solutions to the Allen-Cahn equation in R^3, Adv. Math. 320 (2017), 926–992.

Gui, Changfeng; Liu, Yong; Wei, Juncheng, On variational characterization of four-end solutions of the Allen-Cahn equation in the plane, J. Funct. Anal. 271 (2016), no. 10, 2673–2700.

Kowalczyk, Michał; Liu, Yong; Pacard, Frank; Wei, Juncheng, End-to-end construction for the Allen-Cahn equation in the plane, Calc. Var. Partial Differential Equations 52 (2015), no. 1-2, 281–302.

Kowalczyk, Michał; Liu, Yong; Wei, Juncheng, Singly periodic solutions of the Allen-Cahn equation and the Toda lattice, Comm. Partial Differential Equations 40 (2015), no. 2, 329–356.

Kowalczyk, Michał; Liu, Yong; Pacard, Frank, Multiple end solutions to the Allen-Cahn equation in R^2, Éditions de l'École Polytechnique, Palaiseau, 2014, Exp. No. X, 19 pp. ISBN: 978-2-7302-1633-3.

Kowalczyk, Michał; Liu, Yong; Pacard, Frank, The classification of four-end solutions to the Allen-Cahn equation on the plane, Anal. PDE 6 (2013), no. 7, 1675–1718.

Kowalczyk, Michał; Liu, Yong; Pacard, Frank, Towards classification of multiple-end solutions to the Allen-Cahn equation in R^2, Netw. Heterog. Media 7 (2012), no. 4, 837–855.

Kowalczyk, Michał; Liu, Yong; Pacard, Frank, The space of 4-ended solutions to the Allen-Cahn equation in the plane, Ann. Inst. H. Poincaré C Anal. Non Linéaire 29 (2012), no. 5, 761–781.

Kowalczyk, Michał; Liu, Yong, Nondegeneracy of the saddle solution of the Allen-Cahn equation, Proc. Amer. Math. Soc. 139 (2011), no. 12, 4319–4329.

Liu, Yong, Even solutions of the Toda system with prescribed asymptotic behavior, Commun. Pure Appl. Anal. 10 (2011), no. 6, 1779–1790.

Liu, Yong, Morse homology of super-quadratic Hamiltonian systems on R^{2n},J. Math. Anal. Appl. 344 (2008), no. 1, 384–407.

Liu, Yong; Jiang, Mei-Yue, Periodic bounce solutions of Hamiltonian systems in bounded domains, Adv. Nonlinear Stud. 7 (2007), no.4, 533–550.