Chao Liu (刘 超)

Associate professor

Center for Mathematical Sciences and School of Mathematics and Statistics
Huazhong University of Science and Technology,
1037 Luoyu Road, 
Wuhan, Hubei Province,
China

Office: Math center 813, Enming Biulding

E-mail: chao_liu@hust.edu.cn

HomePage

Self Introduction

  1. 2019.10-now. Associate professor, Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology
  2. 2017.10-2019.9. Postdoc, International Center for Mathematical Research (BICMR), Peking University. Supervisor: Prof. Gang Tian.
  3. 2014.2-2017.9. PhD, School of Mathematics, Monash University. Supervisors: Prof. Todd A. Oliynyk (main) and Dr. Julie Clutterbuck (associate).

Research Interests

Mathematical General Relativity; Hyperbolic Partial Differential Equations; Einstein-matter Equations; Euler-Poisson Equations; Cosmology; A-harmonic Equations

Publications and Preprints

Preprints: 

  1. Fully nonlinear gravitational instabilities for expanding spherical symmetric Newtonian universes with inhomogeneous density and pressure. arXiv:2305.13211. 

  2. Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability. arXiv:2208.06788. 

  3. (With Jinhua Wang) A new symmetric hyperbolic formulation and the local Cauchy problem for the Einstein-Yang-Mills system in the temporal gauge. arXiv:2111.04540v2. 
  4. Localized continuation criterion, improved local existence and uniqueness for the Euler-Poisson system in a bounded domain. arXiv:2111.11708. 

Publications: 

  1. (With Todd A. Oliynyk, Jinhua Wang) Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4.
    Journal of the European Mathematical Society (JEMS), Accepted in December 2023.  arXiv:2202.05432. 
  2. Fully nonlinear gravitational instabilities for expanding Newtonian universes with inhomogeneous pressure and entropy: Beyond the Tolman's solution.
    Physical Review D (PRD), 2023, 107(12): 123534. DOI: 10.1103/PhysRevD.107.123534.  arXiv:2210.04657. 
  3. Blowups and longtime developments with near-boundary mass accretions of irregularly-shaped Euler-Poisson dominated molecular clouds in astrophysics.
    SIAM Journal on Mathematical Analysis (SIMA), 2023, 55, 2553-2594, DOI: 10.1137/22M1469420.  arxiv:2102.11550v2. 

  4. (With Yiqing Shi) Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe.
    Physical Review D (PRD), 2022, 105(4): 043519. DOI: 10.1103/PhysRevD.105.043519.  arXiv:2201.01199. 

  5. (With Changhua Wei) Future stability of the FLRW spacetime for a class of perfect fluids.
    Annales Henri Poincaré (AHP), Springer Nature, 2021, 22(3), 715-770, DOI: 10.1007/s00023-020-00987-1.  arxiv:1810.11788. 

  6. (With Todd A. Oliynyk) Newtonian limits of isolated cosmological systems on long time scales.
    Annales Henri Poincaré (AHP), Springer Nature, 2018, 19, 2157-2243.  DOI: 10.1007/s00023-018-0686-2. arXiv: 1701.03975 
  7. (With Todd A. Oliynyk) Cosmological Newtonian limits on large spacetime scales. 
    Communications in Mathematical Physics (CMP); 2018, 364(3) 1195-1304.  DOI:10.1007/s00220-018-3214-9. arXiv:1711.10896

  8. (With Hongya Gao, Hong Tian) A Generalization of Exponential Class and Its Applications.
    Abstract and Applied Analysis; 2013, Article ID 476309.   DOI:10.1155/2013/476309. arXiv:1812.07843
  9. (With Hongya Gao, Hong Tian) Remarks on a Paper by Leonetti and Siepe.
    Journal of Mathematical Analysis and Applications (JMAA). 2013 (401), 881-887. DOI:10.1016/j.jmaa.2012.12.037,  arXiv:1812.07740

  10. (With Hongya Gao, Junwei Li) Hölder Continuity and Differentiability Almost Everywhere of (K1, K2 )-Quasiregular Mappings.
    Acta Mathematica Sinica Chinese Series，2012,55(4), 721-726.  Journal. arXiv: 1812.07779 

PhD Thesis: 

Cosmological Newtonian Limits on Large Scales, Ph.D. Thesis (2018), Monash University, Melbourne, Australia, available on figshare, 216 pages. 

Teachings

  1. Equations of Mathematical Physics and Special Functions (MAT0701), 2020 (Spring, videos), 2021 (Spring), 2022 (Spring), 2023 (Spring, videos; Fall, videos), 2024 (Spring, videos)
  2. Equations of Mathematical Physics (PHY0721), 2021 (Spring).
  3. Blowup for Nonlinear Hyperbolic Equations, 2020 (Math Center, Sep.).
  4. Minicourse on Sobolev Spaces, 2020 (Math center, Jan.);

Postgraduate Students

  1. Yiqing Shi (时昳晴, PhD,2020-now), Weiqi Ji (纪玮琦, 2022-now), Chihang He (何池航, 2023-now), Chenxinyu Luo (罗辰新宇, 2023-now);

Talks

  1. Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n ≥ 4, Teachers forum, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 25, April, 2024;
  2. Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n ≥ 4, Tianyuan Mathematical Center in Central China, Wuhan Unviersity, Wuhan, 1, March, 2024. Slides;
  3. On the nonlinear gravitational instabilities for Newtonian universes, Mathematical Relativity Seminar, Sun Yat-sen University, Guangzhou, 21, May, 2023. Slides;
  4. Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n ≥ 4, College of Mathematics and Information Science, Hebei Unviersity, Baoding, 10, November, 2022;
  5. Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n ≥ 4, School of Science, Northwest Unviersity, Xi'an, 30, June, 2022;
  6. Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n ≥ 4, School of Science, Tianjin Unviersity of Technology, Tianjin, 20, April, 2022;
  7. Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n ≥ 4, Black Hole Initiative, Harvard University, CMSA General Relativity Seminar, 14, April, 2022, video. Slides;
  8. Blowups and long-time evolution of irregularly-shaped molecular clouds, National University of Singapore, Singapore, 28, April, 2021;
  9. Blowups and long-time evolution of irregularly-shaped molecular clouds, Tianjin University, Tianjin, 23, April, 2021;
  10. Blowups and long-time evolution of irregularly-shaped molecular clouds, Sichuan Normal University, Chengdu, 15, January, 2021;
  11. Blowups and long-time evolution of irregularly-shaped molecular clouds, 2020 Conference on Geometric Analysis and Hyperbolic Equations, Guangxi University, Nanning, 21, December, 2020;
  12. Blowups and long-time evolution of irregularly-shaped molecular clouds, Hohai University, Nanjing, 24, October, 2020;
  13. Mathematical General Relativity and Cosmology, School of Physics, Huazhong University of Science and Technology, Wuhan, 18, September, 2020;
  14. Stability of FLRW metric for polytropic (Makino) fluids, Institut Mittag-Leffler, Djursholm, Sweden, 03, December, 2019. Slides;
  15. Cosmological Newtonian limits, Workshop on PDEs and harmonic analysis, Institute of Applied Physics and Computational Mathematics, Beijing, China, 13th, July, 2019. Slides;
  16. How a Star is Born: Makino’s conjecture and freely falling boundary problem, Workshop on PDEs and mathematical physics 2019, Guizhou Minzu University, Guiyang, China, 12th, May, 2019;
  17. Some aspects of Einstein-Euler equatons, Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, China, 15th, December, 2018;
  18. FLRW-like cosmology can be approximated by Newtonian universe, Workshop on geometric analysis and hyperbolic equations 2018, University of Chinese Academy of Sciences, Beijing, China, 18th, October, 2018; 
  19. Cosmological global evolutions driven by dark energy--A model described by Einstein-Euler equations, Prof. Tian's seminar, BICMR, Peking University, Beijing, China, 25th, September, 2018;
  20. Cosmological Newtonian limits, Zhejiang Sci-Tech University, Hangzhou, China, 26th, June, 2018;
  21. Cosmological Newtonian limits on large scales, BICMR, Peking University, Beijing, China, 27th, December, 2017;
  22. Cosmological Newtonian limits on large scales, Xiamen University, Xiamen, China, 19th, September, 2017; 
  23. Long time cosmological Newtonian limits,  The 60th annual meeting of the AustMS, Australian National University, Canberra, Australia, 7th, December, 2016. 
  24. A time singular symmetric hyperbolic system with a singular parameter, APDEG seminar, Melbourne, Victoria, Australia, Monash University, 20th, September, 2016. ; 
  25. Long-Time Cosmological Newtonian Limits, Workshop on Analysis, Geometry and Mathematical Relativity, Melbourne, Victoria, Australia, Monash University, 22nd February, 2016 - 26th February, 2016. ;
  26. Long Time Existence of Cosmological Newtonian Limits for Einstein-Euler Systems with Positive Cosmological Constant (Conformal Method), Conference in Mathematical General Relativity 2016, Tsinghua Sanya International Mathematics Forum, Sanya, Hainan, China，5th January, 2016 - 9th January, 2016;
  27. Long time behavior of the Einstein-Euler system with Newtonian limit, 8th Australia New Zealand Mathematics Convention, University of Melbourne, Melbourne, Australia, 9th December, 2014.

Visiting Programmes

  1. Institut Mittag-Leffler "GENERAL RELATIVITY, GEOMETRY, AND ANALYSIS: BEYOND THE FIRST 100 YEARS AFTER EINSTEIN",Djursholm, Sweden,September – December 2019;
  2. Erwin Schrödinger Institute "GEOMETRY AND RELATIVITY PROGRAM ", Vienna, Austria, July – August 2017;
  3. Institut Henri Poincaré "MATHEMATICAL GENERAL RELATIVITY PROGRAM ", Paris, France, September – November 2015.

Links

My ORCID
My Researchgate
My ArXiv