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Faculty

Huicheng Yin Professor

Bio: 

Educational Background

  • PhD, Mathematics, Nanjing University (1992)
  • MA, Mathematics, Nanjing University (1989)
  • BA, Mathematics, Nanjing University (1986)

 

Professional Experiences

  • Sep.1992-Dec.1994, Post-doctor, Department of Physics, Nanjing University, China;
  • Jan.1995-Sep.2004, Teacher, Department of Mathematics, Nanjing University, China;
  • Sep.2004-present, Teacher, School of Mathematical Sciences, Nanjing Normal University;

 

Experiences as Visiting Scholar

  •  May-Aug.1999, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Jan.-Feb.2000, Torino University of Italy and Paderborn University of Germany;
  • Mar.-May 2000, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Feb.-Apr.2001, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Jan.-Feb.2002, Institute of Mathematics, Potsdam University, Germany;
  • Mar.-May 2002, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Jan.-Jun.2003, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Sep.2004-Feb.2005, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Jan.-April,Jun.2006, Institute of Mathematical Sciences, The Chinese University of Hongkong;
  • Aug.2007,  Department of Mathematics, National University of Singapore, Singapore;
  • Jan.2008-Feb.2008, Institute of Mathematical Sciences, The Chinese University of HongKong, HongKong;
  • Jan.2009-Feb.2009, Institute of Mathematical Sciences, The Chinese University of HongKong, HongKong;
  • Jan.2010-Feb.2010, Institute of Mathematical Sciences, The Chinese University of HongKong, HongKong;
  • July 2011-Aug.2011, Gottingen University, Germany;
  • July 2012-Aug.2012, Gottingen University, Germany;
  • Jan.2013-Feb.2013, Institute of Mathematical Sciences, The Chinese University of Hong Kong;
  •  Feb.2013-Mar.2013, Gottingen University, Germany;
  • Jan.2014-Feb.2014, Department of Mathematics, City University of Hong Kong, Hong Kong;
  • July 2014-Aug.2014, Institute of Mathematical Sciences, The Chinese University of Hong Kong;
  • Jan.2015-Feb.2015, Department of Mathematics, City University of Hong Kong, Hong Kong;
  • June 2015-July 2015, Department of Mathematics, Nates University, France;
  • Aug.2016, Institute of Mathematical Sciences, The Chinese University of Hong Kong 

  

Research

Research Interests

Nonlinear Partial Differential Equations, Fluid Dynamics

 

Research Projects

2016.1-2019.12,  No.11571177, The studies on the solutions of nonlinear multidimensional hyperbolic equation (NNSF of China)

 

Journal Articles(Selected, 1999-present

  1. On the global solution problem of semilinear generalized Tricomiequations,I, Calc. Var. Partial Differential Equations, 2016,(to appear)  (Joint with  He Daoyin and Witt Ingo)      
  2. Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations ,  Commun. Pure Appl. Anal.,2016,(to appear)  (Joint with Ding Bingbing and Witt Ingo)
  3. Large time asymptotic behavior of the compressible Navier-Stoke equations in partial space-periodic domains, Acta Mathematica Scientia, 36B(4):1167-1191(2016) (Joint with Cao Zhengzi, Zhang Lin and Zhu Lu)
  4. The small data solutions of general 3-D quasilinear wave equations. II, J. Differential Equations 261,  no.2,1429 -1471 (2016) (Joint with Ding Bingbing and Witt Ingo)
  5. The global stability of 2-D viscous axisymmetric circulatory  flows, Discrete and Continuous Dynamical System - A, 2016 (to appear) (Joint with Zhang Lin)
  6. The small data solutions of general 3-D quasilinear wave equations. I, SIAM Journal on Mathematical Analysis, Vol.47, No.6, 4192-4228 (2015) (Joint with Ding Bingbing and Liu Yingbo)
  7. On the instability problem of a 3-D transonic oblique shock wave, Advances in Mathematics 282, 443–515 (2015) (Joint with Li Liang and Xu Gang)
  8. Blowup of classical solutions for 2-D quasilinear wave equations with small initial data, Quart. Appl. Math., Vol.73, No.4, 773-796 (2015) (Joint with Ding Bingbing and Witt Ingo)
  9. On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains, J. Differential Equations, 259, no. 12, 7406-7462  (2015)  (Joint with Ruan Zhuoping and Witt Ingo)
  10. On global multidimensional supersonic flows with vacuum states at infinity, Arch.Ration.Mech.Anal. Vol.218, No.3, 1189-1238 (2015) (Joint with Xu Gang)
  11. On the blowup and lifespan of smooth solutions to a class of 2-D  nonlinear wave equations with small initial data, Quart. Appl. Math., 73,no.2, 219–251(2015) (Joint with Li Jun and Witt Ingo)
  12. Blowup of classical solutions for a class of 3-D quasilinear wave equations with small initial data, Differential Integral Equations , Volume 28, No.9-10, 941-970 (2015) (Joint with Ding Bingbing and Witt Ingo)  
  13. The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases,J. Differential Equations 258, no.2, 445-482 (2015)  (Joint with Ding Bingbing and Witt Ingo)
  14. On the existence and cusp singularity  of solution to semilinear generalized Tricomi equation with discontinuous initial  data, Communications in Contemporary Mathematics, Vol.17, No.3, 1450028 (49 pages) 2015 (Joint with Ruan Zhuoping and Witt Ingo)
  15. Nodal solutions of 2-D critical nonlinear Schrodinger equations with potentials vanishing at infinity, Discrete and Continuous Dynamical System - A 35-7, 2921–2948 (2015)(Joint with Fei Mingwen)
  16. A Liouville type theorem for subsonic flows around an infinite long ramp,  Quart. Appl. Math., 72,no.2, 253-265 (2014) (Joint with Yang Hui)
  17. On the global existence and stability of a three-dimensional supersonic conic shock wave, Comm.Math.Phys. 329,609-640 (2014)
  18. The singularity structures of low regularity solutions to higher order degenerate hyperbolic equations, J. Differential Equations 256, No.2, 407–460 (2014) (Joint with Ruan Zhuoping and Witt Ingo)
  19. Bound states of 2-D critical nonlinear Schrodinger equations with potentials tending to zero at infinity, SIAM J.Math.Anal. 45(4),2299-2331(2013) (Joint with FeiMingwen)
  20. A transonic shock in a general two-dimensional De Laval nozzle,Archive for Rational Mechanics and Analysis ,Vol.207, No.2, 533-581 (2013) (Joint with Li Jun & Xin Zhouping) 
  21. Bound states of asymptotically linear Schr\"{o}dinger equations with compactly supported potentials,Pacific J. Math. 261,no.2,335–367(2013) (Joint with Fei Mingwen)
  22. On the blowup of classical solutions to the 3-D pressure-gradient systems, J. Differential Equations 252,3608–3629 (2012) (Joint with Ding Bingbing) 
  23. Nonexistence of global weak solution with only one stable supersonic conic shock wave for the steady supersonic Euler flow past a perturbed cone, Quart. Appl. Math.,Vol.LXX, No.2, 199-218 (2012) (Joint with Xu Gang)
  24. The monotonicity and  uniqueness of a 3-D transonic shock solution in a conic nozzle with variable end pressure, Pacific J Math.,Vol.254, No.1, 129-171  (2011) (Joint with Li Jun  & Xin Zhouping)
  25. On the nonexistence of a global nontrivial subsonic  solution in a  3-D unbounded angular domain, Sci.China Ser.A, Vol.53,No.7,1753 -1766 (2010) (Joint with Li Jun and Zhou Chunhui)
  26. The existence and monotonicity of a 3-D transonic shock in a finite  nozzle with the axisymmetric exit pressure, Pacific J Math., Vol.247, No.1, 109-162  (2010) (Joint with Li Jun  & Xin Zhouping)
  27. Local Structural Stability of A Multidimensional Centered Rarefaction Wave for the 3-D Steady Supersonic Euler Flow Around a Sharp Corner, SIAM J.Math.Anal., Volume 42, Issue 4, 1639-1687 (2010) (Joint with Wang Zhan)
  28. Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone, Nagoya J Math, Vol. 199, 151-181(2010) (Joint with Xu Gang)
  29. On existence and concentration of bound states  of nonlinear Schrodinger equations with compactly supported  and competing  potentials, Pacific J.Math.,  Vol.244, No.2, 261-296 (2010)  ( Joint with Fei Mingwen)
  30. On transonic shocks in a conic divergent nozzle with axisymmetric exit pressures,J.Differential Equations 248(2010),423-469 (Joint with Li Jun  & Xin Zhouping)
  31. On the existence and stability of a global subsonic flow in a 3-D infinitely long cylindrical nozzle, Chin. Ann. Math. Ser. B 31 (2), 163-190 (2010) ( Joint with Xu Gang)
  32. A free boundary value problem for the full Euler system and 2-D transonic shock in a large variable nozzle, Math.Res.Lett.,Vol.16,No.5,779-798(2009)( Joint with Li Jun  & Xin Zhouping)
  33. Bound states of nonlinear Schrodinger equations with potentials  tending to zero at infinity, J.Differential Equations 247, 618- 647  (2009)  (Joint with Zhang Pingzheng)
  34. On transonic shocks in a 2-D nozzle with variable end pressures, Comm.Math.Phys. 291,111-150(2009) (Joint with Li Jun  & Xin Zhouping)
  35. On global transonic shocks for the steady supersonic Euler flows past sharp 2-D wedges, J.Differential Equations 246,4466-4496 (2009) (Joint with Zhou Chunhui)
  36. Transonic shock problem for the Euler system in a nozzle, Arch.Ration. Mech.Anal.,194,1-47(2009)(Joint with Xin Zhouping & Yan Wei)
  37. Global supersonic conic shock wave for the steady flow past a cone, J. Differential Equations 246 , 641-669 (2009) (Joint with Cui Dacheng)
  38. Global multidimensional transonic conic shock wave for the perturbed supersonic flow past a cone, SIAM J.Math.Anal.,Vol.41, No.1, 178-218(2009) (Joint with Xu Gang)
  39. The transonic shock in a nozzle, 2-D and 3-D complete Euler systems, J. Differential Equations 245 , no. 4, 1014-1085 (2008) (Joint with Xin  Zhouping)
  40. A note on the elliptic equation method, Commun. Nonlinear Sci. Numer. Simul. 13 , no. 3, 547-553 (2008) (Joint with Chen Huaitang)
  41. 3-Dimensional transonic shocks in a nozzle, Pacific J.Math. 236 , no. 1, 139-193(2008)(Joint with Xin Zhouping)
  42. The uniqueness of a transonic shock in a nozzle for the 2-D complete Euler system with the variable end pressure, J. Partial Differential Equations 21,no.3, 263-288(2008) (Joint with Cui Dacheng)
  43. Global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone, J.Differential Equations245 , 3389 -3432 (2008) (Joint with Xu Gang)
  44. Global conic shock wave for the steady supersonic flow past a cone: Isothermal case, Pacific J.Math., Vol.233, No.2,257-289(2007) (Joint with Cui Dacheng)
  45. The weighted $W\sp {2,p}$ estimate on the solution of the Gellerstedt equation in the upper half space, J. Math. Anal. Appl. 332, no. 2, 1148-1164 (2007) (Joint with Xu Ning)
  46. Double elliptic equation method and new exact solutions of the (n+1)-dimensional sinh-Gordon equation, J. Math. Phys. 48 (2007), no.1, 013504, 7 pp. (Joint with Chen Huaitang)
  47. Global existence of a shock for the supersonic flow past a curved wedge, Acta Math. Sin. (Engl. Ser.) 22, no. 5, 1425-1432 (2006)
  48. Global multidimensional shock wave for the steady supersonic flow past a three-dimensional curved cone, Anal. Appl. (Singap.) 4, no. 2, 101-132 (2006) (Joint with Xin Zhouping)
  49. Global singularity structures of weak solutions to 4-D semilinear dispersive wave equations, Math. Z. 252, no. 2, 231-249 (2006) (Joint with Xu Ning)
  50. On the singularities of solutions to 4-D semilinear dispersive wave equations, Anal. Theory Appl. ,no. 2, 176-18721 (2005) (Joint with Xu Ning)
  51. Transonic shock in a nozzle. I. Two-dimensional case, Comm. Pure Appl. Math. 58, no. 8, 999-1050 (2005) (Joint with Xin Zhouping)
  52. Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data, Nagoya Math.J. 175, 125-164(2004)
  53. Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data, J. Differential Equations 196, no. 1, 134-150 (2004) (Joint with Ingo Witt)
  54. Long shock for the supersonic flow past a multidimensional pointed body, AMS/IP Stud.Adv.Math.,29, Amer.Math. Soc., Providence, RI, 207-215(2002)
  55. The blowup for 2-D quasilinear wave equations with cubic nonlinearity, Sci.in China, Vol.45, No.3, 307-320(2002)
  56. The global shock waves for the supersonic flow past a curved cone,Comm. Math.Phys.,Vol.228,47-84(2002) (Joint with Chen Shuxing & Xin Zhouping)
  57. The geometric blowup of solutions for two dimensional irrotational Euler  equation with small perturbed initial data, Acta Math.Sinica, English Series, Vol.18, No.2, 217-228(2001)
  58. The blowup mechanism of small data solution for the quasilinear wave equations in three space dimensions, Acta.Math.Sinica,English Series,Vol.18, No.1,35-76(2001)
  59. The asymptotic behaviour of solutions for a class of quasilinear wave equations with cubic nonlinearity in two space dimensions, Acta Math.Appl. Sinica, Vol.16,No.3,299-312(2000)
  60. The geometric blowup of 3-D quasilinear wave equations with small axisymmetric initial data, Sci.in China,Vol.43,No.3,252-266(2000)
  61. The blowup of solutions for 3-D axisymmetric compressible Euler Equations, Nagoya Math.J.,Vol.154,157-169(1999) (Joint with Qiu Qingjiu)
  62. The blowup of radially symmetric solutions for 2-D quasilinear wave equations  with cubic nonlinearity, Chin.Ann.Math.B, 18(4), 455-472 (1999)
  63. The uniform existence of solutions for two dimensional and three dimensional semilinear  wave equations with oscillatory data, Proc.A.M.S., Vol.127, No.1, 195-198(1999)

 

Preprints:

  1. A global multidimensional shock wave for 2-D and 3-D unsteady potential flow equations (Joint with Li Jun and Witt Ingo)
  2. Behavior of compressible fluid  in an infinitely  expanding ball, 3D Euler equations (Joint with  Xu Gang and Yang Tong)
  3. Global smooth compressible fluids  in infinitely  expanding balls, 3D Navier-Stokes equations (Joint with  Yang Tong and Zhang Lin)
  4. Global existence or blowup of smooth solutions to 3-D compressible Euler equations with time-depending damping (Joint with Hou Fei and Witt Ingo)
  5. On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping (Joint with Hou Fei)
  6. On the steady non-Newtonian fluids in the domains with noncompact boundaries (Joint with  Yang Jiaqi)
  7. On the global solution problem of semilinear generalized Tricomi equations, II (Joint with  He Daoyin and Witt Ingo)
  8. On the global existence and stability of 3-D viscous cylindrical circulatory  flows (Joint with Zhang Lin)
  9. Minimal regularity solutions  of  semilinear   generalized Tricomi equations (Joint with Ruan Zhuoping and Witt Ingo)
  10. On the global existence and stability of 3-D viscous cylindrical circulatory  flows (Joint with Zhang Lin)
  11. Global smooth compressible fluids  in infinitely  expanding balls,  Boltzmann equation (Joint with  Yang Tong and Zhao Wenbin)

 

Contact :

Email:05407@njnu.edu.cn, huicheng@nju.edu.cn