Personal Profile
Cao Gaowei currently serves as Associate Research Fellow at the Hetao Institute of Mathematics and Interdisciplinary Sciences (Shenzhen). He obtained his undergraduate degree from the Department of Mathematics at Zhengzhou University and his doctoral degree from the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, under the supervision of Research Fellow Yang Xiaozhou.
His research primarily focuses on the mathematical theory of nonlinear partial differential equations, encompassing nonlinear hyperbolic conservation laws, Euler/Euler-Poisson equations in fluid dynamics, and stochastic differential equations. Current research interests centre on the formulation and representation of smooth/entropy solutions, the refined properties of solutions, and the construction of nonlinear fundamental waves.
He has undertaken multiple academic visits abroad, including a one-year visit to Professor Chen Guiqiang, Chair Professor at the University of Oxford, from 2022 to 2023. He has led projects such as the National Natural Science Foundation of China Young Scientist Fund and the Chinese Academy of Sciences Multidisciplinary Cross-disciplinary Project. He has published over ten papers in domestic and international mathematical journals. He previously served as Associate Researcher at the Chinese Academy of Sciences Precision Measurement Science and Technology Innovation Institute (formerly the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences).
Research Interests
His primary research domain lies in the mathematical analysis of nonlinear partial differential equations, with particular focus on hyperbolic conservation laws, Euler/Euler-Poisson systems, Hamilton-Jacobi equations, stochastic partial differential equations, and combustion models. His recent research interests centre on: entropy solutions and their refined properties for scalar hyperbolic conservation laws, zero-pressure Euler/Euler-Poisson systems, and stochastic conservation laws. These include: local fine structure, global structure, and asymptotic behaviour; as well as invariant measures, entropy conditions, smooth solution expressions, and the non-self-similar structure of Riemann solutions.
Educational Background
2009.09--2014.06 University of Chinese Academy of Sciences Doctor of Philosophy in Science
2005.09--2009.06 Bachelor of Science, Zhengzhou University
Work Experience
2017.10--2025.09 Associate Research Fellow Institute of Precision Measurement Science and Technology Innovation, Chinese Academy of Sciences (formerly Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)
2014.07--2017.09 Assistant Research Fellow Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences
Academic visit
March 2025 – April 2025 Visiting Researcher, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Huang Feimin
January 2025 – January 2025 Visiting Researcher, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Huang Feimin
July 2024 – September 2024 Visiting Researcher, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Huang Feimin
2022.07–2023.07 Visiting the Department of Mathematics, University of Oxford (OxPDE Centre) 1 year Chen Guiqiang
2018.10–2018.11 Visiting the Department of Mathematics, City University of Hong Kong Xiang Wei
2017.06–2017.08 Visiting Scholar, Department of Mathematics, City University of Hong Kong Xiang Wei
2016.10–2016.11 Visiting Scholar, Department of Mathematics, City University of Hong Kong Xiang Wei
2015.11–2016.01 Visiting Scholar, Department of Mathematics, City University of Hong Kong Xiang Wei
Honours and Awards
In 2013, he was awarded the Wang Tianjuan Prize by the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences.
In 2014, awarded the Zhu Liyuehua Prize for Outstanding Doctoral Students by the Chinese Academy of Sciences.
Publications
[1] Gaowei Cao, Feimin Huang, and Guirong Tang, Formula for Entropy solutions for the one-dimenional Pressureless Euler-Poisson System: Well-posedness of Entropy Solutions and the Asymptotic Behaviors, accepted by Proceedings of the Steklov Institute of Mathematics, 2025.
[2] Gaowei Cao and Gui-Qiang G. Chen, Minimal entropy conditions for scalar conservation laws with general convex fluxes, Quarterly of Applied Mathematics. 81(3) (2023), 567-598.
[3] Gaowei Cao, Hui Kan, Wei Xiang, and Xiaozhou Yang, Smooth solution of multi-dimensional non-homogeneous conservation law: its formula, and necessary and sufficient blowup criterion, Acta Math. Appl. Sin., Engl. Ser. 39(1) (2023), 17–27.
[4] Guiqin Qiu, Gaowei Cao, Xiaozhou Yang, and Yuan-An Zhao, Envelope methods and more general new global structures of solutions for multi-dimensional conservation law, Commun. Appl. Math. Comput. 5(3) (2023), 1180-1234.
[5] Guiqin Qiu, Gaowei Cao, and Xiaozhou Yang, Structures of interaction of non-selfsimilar elementary waves for 2D scalar conservation law with two initial discontinuities, Acta Math. Appl. Sin., Engl. Ser. 39(3) (2023), 465-490 .
[6] Yuan-An Zhao, Gaowei Cao, and Xiaozhou Yang, Global solutions and interactions of non-selfsimilar elementary waves for n-D non-homogeneous Burgers equation, Acta Math. Appl. Sin., Engl. Ser. 39(4) (2023), 830-853.
[7] Gaowei Cao, Wei Xiang, and Xiaozhou Yang, Global structure of admissible solutions for multi-dimensional non-homogeneous scalar conservation law with Riemann-type data, J. Differential Equations. 263(2) (2017), 1055-1078.
[8] Kai Hu, Gaowei Cao, and Xiaozhou Yang, Non-selfsimilar global solutions and their structure for the multi-dimensional combustion models, Acta Math. Appl. Sin., Engl. Ser. 33(3) (2017), 659-678.
[9] Gaowei Cao, Kai Hu, and Xiaozhou Yang, Envelope and classification of global structures of solutions for a class of two-dimensional conservation laws, Acta Math.Appl. Sin., Engl. Ser. 32(3) (2016), 579-590.
[10] Chunlong Yang, Gaowei Cao, and Xiaozhou Yang, Uniform formula for the Riemann solutions of a scalar combustion model, Acta Math. Sci., Engl. Ed. 36B(5) (2016), 1405-1418.
[11] Gaowei Cao, Kai Hu, and Xiaozhou Yang, A formula of global smooth solution for non-homogeneous multi-dimensional conservation laws with unbounded initial value, Acta Math. Sci., Engl. Ed. 35B(2) (2015), 508-526.
[12] Kai Hu, Gaowei Cao, and Xiaozhou Yang, Riemann problems for three-dimensional combustion models, Acta Math. Appl. Sin., Engl. Ser. 30(2) (2014), 321-346.