Research Interest
Research Interest
Nonlinear partial differential equations
Calculus of variations
Geometric measure theory
Static and hydrodynamic theories of liquid crystals
Free boundary problems
Phase Transition Models
Fluid dynamics
Zhiyuan Geng, Changyou Wang. Eigenframe discontinuities of the Q-tensor model. (2025), to appear in Calc. Var. Partial Differ. Equ..
Zhiyuan Geng. Rigidity results for a triple junction solution of Allen-Cahn system. (2024), to appear in SIAM J. Math. Anal..
Zhiyuan Geng, Changyou Wang, Junao Yu. On forward self-similar heat flow of harmonic maps. (2024), to appear in Manuscripta Math. .
Zhiyuan Geng. Uniqueness of the blow-down limit for triple junction problem. (2024) Comm. Pure Appl. Math., 78(2025), 500--534.
Zhiyuan Geng, Wei Wang. Point defects in 2-D liquid crystals with singular potential: profiles and stability. Sci. China Math. (2024), 1-26.
Zhiyuan Geng, Arnab Roy, Arghir Zarnescu. Global existence of weak solutions for a model of nematic liquid crystal-colloidal interactions. SIAM J. Math. Anal., 56 (2024), 4324-4355.
Nicholas D. Alikakos and Zhiyuan Geng. On the triple junction problem without symmetry hypotheses. Arch. Ration. Mech. Anal., 248 (2024).
Zhiyuan Geng, Arghir Zarnescu. Uniform profile near the point defect of Landau-de Gennes model. Calc. Var. Partial Differ. Equ., 62(2023).
Nicholas D. Alikakos, Zhiyuan Geng, Arghir Zarnescu. Asymptotic behavior of the free interface for entire vector minimizers in phase transitions. J. Funct. Anal., 283 (2022).
Zhiyuan Geng , Rafael Granero-Belinchón. A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows. Proc. Amer. Math. Soc., 151 (2023), 707-722.
Zhiyuan Geng, Fanghua Lin. The Two-Dimensional Liquid Crystal Droplet Problem with a Tangential Boundary Condition. Arch. Ration. Mech. Anal., 243 (2021), 1181-1221.
Zhiyuan Geng, Fanghua Lin. Large m asymptotics for minimal partitions of the Dirichlet eigenvalue. Sci. China Math., 65 (2022), 1-8.
Zhiyuan Geng, Jiajun Tong. Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions. Calc. Var. Partial Differ. Equ., 59 (2020), 1-35.
Zhiyuan Geng, Wei Wang, Pingwen Zhang, Zhifei Zhang. Stability of half-degree point defect profilesfor 2-D nematic liquid crystal. DCDS-A, 37 (2017) , 6227-6242.
Zhiyuan Geng. Asymptotics for 2D Allen-Cahn minimizers. In preparation.
Zhiyuan Geng. Half-space minimizing solutions of 2D Allen-Cahn system. In preparation.
Zhiyuan Geng and Changyou Wang. Weighted Energy-Dissipation for wave maps. In preparation.
Zhiyuan Geng, Razvan-Dumitru Ceuca, Arnab Roy, Arghir Zarnescu. Global existence of weak solutions for a model of nematic liquid crystal-colloidal interactions with general boundary conditions. In preparation.
Nov. 2025, Workshop: “New trends in elliptic and parabolic equations”, BIRS, Banff.
Sept. 2025, PDE seminar, University of Tennessee Knoxville.
Sept. 2025, PDE, complex analysis and differential geometry seminar, University of Notre Dame.
June 2025, Partial Differential Equations Conference, University of Athens.
May 2025, International Conference on Partial Differential Equations, Shanghai.
Apr. 2025, Analysis and PDE seminar, Johns Hopkins University.
Apr. 2025, AMS Spring Eastern Sectional Meeting, Special Session on "Recent Mathematical Advancement of Topics in Material Science", Hartford.
Mar. 2025, Analysis seminar, University of Oklahoma, Oklahoma City.
Mar. 2025, PDE seminar, Purdue University.
Jan. 2025, Joint Mathematics Meetings, AMS Special Session on "Recent Developments in PDEs and Related Areas", Seattle.
Nov. 2024, Applied Analysis and PDE Seminar, University of Athens (EKPA).
Sept. 2024, PDE Seminar, Purdue University.
Jun. 2024, PDE Seminar, Central South University.
Jun. 2024, PDE Seminar, Hunan University.
Feb. 2024, PDE and Applied Math Seminar, Indiana University Bloomington.
Oct. 2023, PDE Seminar, Purdue University.
Jun. 2023, Zhejiang University Young Scholars Forum on Mathematics, Hangzhou.
Jun. 2023, Young Scholar Forum on Mathematics, Shenzhen University.
Jan. 2023, Workshop: “Current challenges in complex materials: modelling and analysis”, Bonn.
Jun. 2022, 11th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Madrid.
Apr. 2022, Analysis of Nematic Liquid Crystals Flows Workshop, CIRM, Marseille Luminy.
Jan. 2022, Congreso Bienal de la Real Sociedad Matemática Española 2022, Special Session ”Free boundary problems in physics and biology”, Ciudad Real.
Nov. 2021, Analysis Seminar, University of Cantabria.
Jun. 2021, Applied Analysis and PDEs Seminar, University of Athens (EKPA).
May 2021, Analysis Seminar, Zhejiang University.
Sept. 2019, 5th Numerical PDE Workshop, Peking University.
Sept. 2019, Applied and Computational Mathematics PhD Workshop, Peking University.