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 Fall and 2025 Spring Advanced Calculus
Research
interest
Nonlinear PDE and Harmonic Analysis
Plublication
A. Journal Papers
15. (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.
Arch. Rational Mech. Anal., 248 (2024), Article numbr 112
14. (With H.-W. Kuo and M.-H. Liang) Green's function for solving
initial-boundary value problem of
evolutionary partial differential
equations. Int. J. Math. , 34 (2023), 2350049
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. 26 (2024), 1747-1793
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 Schrodinger
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
Schrodinger equation , J.
Differential Equations, 249 (2010) no.10, pp. 2521-2547.
01. Bilinear Strichartz estimates for Schrodinger 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 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
Schrodinger equations, ArXiv:1410.7520