Jin-Cheng Jiang

Professor
Ph.D. Johns Hopkins University
Department of  Mathematics
National Tsing Hua University

R602, General Building III
Phone:03-571-5131 ext  42640
jcjiang  at  math.nthu.edu.tw

Teaching
2024 Spring  Calculus II
                 

Research interest
Nonlinear PDE and Harmonic Analysis

Plublication
A. Journal Papers

14. (With H.-W. Kuo and M.-H. Liang) Green's function for solving initial-boundary value problem of
      evolutionary partial differential equations. International Journal of Mathematics, (2023)

13. (With L.-B. He) On the Cauchy problem for the cutoff Boltzmann equations with small initial data,
      Journal of Statistical Physics, 190 (2023), Article number 52.

12. (With L. Desvillettes and L. He )  A new monotonicity formula for the spatially homogeneous
      Landau equation with Coulomb potential and its applications.  J. Eur. Math. Soc. (2023)

11. (With L.-B. He and Y.-L Zhou)  On the cutoff approximation for the Boltzmann equation
      with long range interaction, Journal of Statistical Physics, 181(2020), 1817-1905.

10. Sharp regularizing estimates for the gain term of the Boltzmann collision operator,
      SIAM J. Math. Anal. 52 (2020) v4 , 4068-4100.

09. (With K. Hidano, S. Lee and C. Wang) Weighted fractional chain rule and nonlinear
      wave equations with minimal regularity, Rev. Mat. Iberoam, 36 (2020),  341-356.

08. (With T.-P.Liu) Boltzmann collision operator for the infinite range potential:a limit problem.
      Ann. Inst. H. Poincare Anal. Non lineaire, 36 (2019) no.6 , 1639-1677.

07. (With L.-B. He) Well-posedness and scattering for the Boltzmann equations:Soft potential
      with cut-off,  Journal of Statistical Physics, 168 (2017) v.2, 470-481.

06. (With S.Shao and C.-K. Lin) On one dimensional Quantum Zakharov system,
      DCDS-A, 36 (2016), 5445-5475.

05. (With S. Shao) On characterization of the sharp Strichartz inequality for the Schrödinger
      Equation, Analysis & PDE, 9 (2016), 353-361.

04. Smoothing property of gain part of Boltzmann collision operator, 
      SIAM J. Math. Anal., 44 (2012),  1522-1543.

03. (With C. Wang and X. Xu ) Generalized and Weighted Strichartz Estimates,
       Comm. Pure Appl. Anal., 11 (2012) no.5, 1723-1752.

02. (With B. Pausader and S. Shao) The linear profile decomposition for the fourth order
      Schrödinger equation , J. Differential Equations, 249 (2010) no.10, pp. 2521-2547.

01.  Bilinear Strichartz estimates for Schrödinger operators in 2 dimensional compact
       manifolds with boundary and cubic NLS, Differential and Integral Equations, 24
     (2011) no.1-2, pp.83-108.

B. Other Papers 


• (With L.-B. He, H.-W. Kuo and M.-H. Liang) The Lp estimate for the gain term of the Boltzmann
     collision operator and its application. ArXiv: 2404.05517

• (With A.V. Bobylev and I.F. Potapenko) On the comparison of Boltzmann and Landau collision
   integrals, Keldysh Institute Preprints, 2019. doi:10.20948/prepr-2019-30-e


• (With L.-B. He) On the gloabl dynamics of the inhomogeneous Boltzmann equations without
      angular cutoff: Hard potential and Maxwellain molecules. ArXiv: 1710.00315.

• (With H.-X Li, H.-C Fu, S.-Y. Huang, D.-M. Kwal, Y.-F Chou) Testing power-delivery TSVs,
   Proceedings of the 6th Asia Symposium on Quality Electronic Design, ASQED 2015 ,
   2015-09-21

• (With S. Shao and B. Stovall ) Linear profile decomposition for a family of 4th order
    Schrödinger equations, ArXiv:1410.7520