Publications

My research is partially supported by NSF grants: DMS-2306258, 2023-2026; DMS-2008504, 2020-2024. DMS-1715012, 2017-2021;

  1. The initial stages of a generic singularity for a 2D pressureless gas, submitted, (with Albeto Bressan and Shoujun Huang).
  2. L2 Stability and weak-BV uniqueness for nonisentropic Euler equations, CPAA, Vol. 3, No. 3, pp. 450-482. (with Alexis Vasseur).
  3. Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry , submitted (with Faris A El-Katri, Yanbo Hu, Yannan Shen).
  4. From Navier-Stokes to BV solutions of the barotropic Euler equations, submitted (with Moon-Jin Kang and Alexis F. Vasseur).
  5. BV solutions to a hyperbolic system of balance laws with logistic growth, J Differential Equations, 392, 128-164(with Yanni Zeng).
  6. Generic Singularities for 2D Pressureless Flow, to appear in Sci. China Math. (with Albeto Bressan and Shoujun Huang).
  7. Initial-boundary value problems for Poiseuille flow of nematic liquid crystal via full Ericksen-Leslie model, SIAM Math. Anal., 56 (2), 1809-1850 (with Yanbo Hu and Qingtian Zhang).
  8. The Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals: The general Case, J. Differential Equations 376, 538-573 (with Weishi Liu and Majed Sofiani).
  9. Lipschitz optimal transport metric for a wave system modeling nematic liquid crystals, SIAM Math. Anal., 56 (4), 5144-5174 (with Hong Cai and Yannan Shen).
  10. Singularity formation for full Ericksen-Leslie system of nematic liquid crystal flows in dimension two, SIAM Math. Anal., 56 (3), 3968-4005 (with Tao Huang and Xiang Xu).
  11. Existence and regularity for global solutions including breaking waves from Camassa-Holm and Novikov equations to lambda-family equations, Quarterly of Applied Mathematics, 81 (4), 751-776, (with Shihui Zhu and Yannan Shen).
  12. Singularity formation for the general Poiseuille flow of nematic liquid crystals, Communications on Applied Mathematics and Computation (by invitation) 5 (2023), no. 3, 1130–1147. (with Majed Sofiani).
  13. Uniqueness and weak-BV stability for 2x2 conservation laws, Arch. Ration. Mech. Anal. 246 (2022), no. 1, 299–332. (with Sam G. Krupa and Alexis F. Vasseur).
  14. Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data, Applied Mathematics Letters 120 (2021), Paper No. 107268, 8. (with Hong Cai and Hongwei Mei).
  15. A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation, J. Differential Equations, 356 (2023), 289–335. (with Hong Cai and Yannan Shen).
  16. Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle, J. Math. Phys. 63 (2022), no. 2, Paper No. 021508, 21. (with Hong Cai, Yi Du and Yannan Shen).
  17. Vanishing Viscosity Limit of the Three-Dimensional Barotropic Compressible Navier-Stokes Equations with Degenerate Viscosities and Far-Field Vacuum, Annales de l'Institut Henri Poincare, Analyse non lineaire. 39 (2022), no 1, 121–170. (with Gui-Qiang Chen and Shengguo Zhu).
  18. Singularity formation for radially symmetric expanding wave of Compressible Euler Equations, to appear in SIAM J. Math. Anal. (with Hong Cai, Tian-Yi Wang).
  19. Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model, submitted, (with Tao Huang, Weishi Liu) Arch. Ration. Mech. Anal. 236 (2020), 839-891.
  20. Formation of Singularities and Existence of Global Continuous Solutions for the Compressible Euler Equations, SIAM J. Math. Anal. 53 (2021), no. 6, 6280–6325 (with Gui-Qiang G. Chen, Shengguo Zhu).
  21. Optimal density lower bound on nonisentropic gas dynamics, J. Differential Equations, 268 (2020), no. 7, 4017-4028.
  22. On finite time BV blow-up for the p-system, Communications in Partial Differential Equations 43 (2018), no. 8, 1242–1280. (with Alberto Bressan and Qingtian Zhang).
  23. A polygonal scheme and the lower bound on density for the isentropic gas dynamics, DCDS 39 (2019), no. 7, 4259-4277. (with Ronghua Pan and Shengguo Zhu).
  24. The almost global existence for a 3-D wave equation of nematic liquid-crystals, (with Yi Du and Jianli Liu). Contemporary Mathematics, volume 725, 2019.
  25. Uniqueness and regularity of conservative solution to a wave system modeling nematic liquid crystal, J. Math. Pures Appl. (9) 117 (2018), 185–220. (with Hong Cai, Yi Du).
  26. Lipschitz metric for the Novikov equation, Arch. Ration. Mech. Anal. 229 (2018), no. 3, 1091–1137 (with Hong Cai, Robin Ming Chen and Yannan Shen).
  27. Generic regularity and Lipschitz metric for the Hunter-Saxton type equations, J. Differential Equations 262, 1023-1063 (2017) (with Hong Cai, Yannan Shen and Zhong Tan).
  28. Lipschitz metric for conservative solutions of the two-component Camassa-Holm system, Z. Angew. Math. Phys. (ZAMP) 68 (2017), no. 1, 5-16 (with Hong Cai and Yannan Shen).
  29. Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation, Indiana Univ. Math. J. 67 (2018), 2393-2433 (with Ming Chen and Yue Liu).
  30. Optimal time-dependent lower bound on density for classical solutions of 1-D compressible Euler equations, Indiana Univ. Math. J., 66 (2017), No. 3, 725–740.
  31. Lipschitz metric for a class of nonlinear wave equations, Arch. Ration. Mech. Anal. 226 (2017) no. 3, 1303–1343 (with Alberto Bressan).
  32. Generic structure of conservative solutions to a nonlinear wave equation, Annales de l'Institut Henri Poincare, Analyse non lineaire. 34 (2017), no. 2, 335–354 (with Alberto Bressan).
  33. Singularity formation for compressible Euler equations, SIAM J. Math. Anal. 49 (2017), no. 4, 2591–2614. (with Ronghua Pan and Shengguo Zhu).
  34. Unique conservative solutions to a variational wave equation, Arch. Ration. Mech. Anal. 217, (2015), no. 3, 1069-1101. (with Alberto Bressan, Qingtian Zhang).
  35. Existence and regularity of solutions in nonlinear wave equations, Discrete Contin. Dyn. Syst., Series A, 35 (2015), no. 8, 3327-3342. (with Yannan Shen).
  36. No BV bounds for approximate solutions to p-system with general pressure law, J. Hyper. Differential Equations, 12(2015), 799-816.(with Alberto Bressan, Qingtian Zhang and Shengguo Zhu).
  37. Finite time singularities for hyperbolic systems, SIAM J. Math. Anal. 47 (2015), no. 1, 758-785, (with Tao Huang and Chun Liu).
  38. Shock formation and exact solutions for the compressible Euler equations, Arch. Ration. Mech. Anal. 217 (2015), no. 3, 1265-1293. (with Robin Young).
  39. Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics, Discrete Contin. Dyn. Syst., Series A, 35 (2015), no. 1, 25-42. (with Alberto Bressan and Qingtian Zhang).
  40. Lack of BV Bounds for Approximate Solutions to the p-system with Large Data, J. Differential Equations 256 (2014), 3067-3085 (with Alberto Bressan and Qingtian Zhang).
  41. No TVD fields for 1-d isentropic gas flow, Comm. Partial Differential Equations, 38 (2013), no. 4, 629-657 (with Helge Kristian Jenssen).
  42. Existence and singularity to a wave system of nematic liquid crystals, J. Math. Anal. Appl., 398 (2013), 170-188 (with Yuxi Zheng).
  43. Shock formation in the compressible Euler equations and related systems, J. Hyper. Differential Equations, 10 (2013), no. 1, 149-172 (with Robin Young and Qingtian Zhang).
  44. Conservation solutions to a system of variational wave equations of nematic liquid crystals, Comm. Pure Appl. Anal., 12 (2013), no. 3, 1445-1468 (with Ping Zhang and Yuxi Zheng).
  45. Pairwise wave interactions in ideal polytropic gases, Arch. Ration. Mech. Anal., 204 (2012), no. 3, 787-836, (with Erik Endres and Helge Kristian Jenssen).
  46. Vacuum in the non-isentropic gas dynamics, Acta Mathematica Scientia, 32 (2012), 339-351, no. 1, (with Robin Young). (Special issue for Constantine M. Dafermos' 70th birthday.)
  47. Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation, J. Differential Equations, 252 (2012), no. 3, 2580-2595, (with Robin Young).
  48. Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations, J. Hyper. Differential Equations, 8 (2011), no. 4, 671-690.
  49. Disease persistence for a kind of age-structured epidemic models (in Chinese), Appl. Math. J. Chinese Univ. Ser. A, 22 (2007), no. 3, 253-262.
  50. SARS epidemic model and its application (in Chinese), Appl. Math. J. Chinese Univ. Ser. A, 21 (2006), no. 3, 253-263, (with Yuanjun Wang).