Publications of Renjun Duan

**Accepted and
Published Research Papers**

1. With Xie Li and Zhaoyin Xiang: Global existence and large time
behavior for a two-dimensional chemotaxis-Navier-Stokes system, accepted for
publication in *Journal of Differential Equations* (2017), http://dx.doi.org/10.1016/j.jde.2017.07.015.
pdf file

2. With Yoshihiro Ueda and Shuichi Kawashima: Decay structure of two
hyperbolic relaxation models with regularity-loss, *Kyoto Journal of
Mathematics*, 57 (2017), no. 2, 235-292. pdf file

3. With Hongjun Yu: The relativistic Boltzmann equation for soft potentials,
*Advances in Mathematics*, 312 (2017), 315-373. pdf file

4. With Feimin Huang, Yong Wang and Tong Yang: Global well-posedness of
the Boltzmann equation with large amplitude initial data, *Archive for Rational
Mechanics and Analysis*, 225 (2017), no. 1, 375-424. pdf file

5. With Yuanjie Lei, Tong Yang, and Hui-Jiang Zhao: The
Vlasov-Maxwell-Boltzmann system near Maxwellians in the whole space with very
soft potentials, *Communications in Mathematical Physics*, 351 (2017), no.
1, 95-153. pdf file

6. With Yong Wang and Tong Yang: Global existence for the ellipsoidal BGK
model with initial large oscillations (in Chinese), *Sci Sin Math*, 47
(2017), 1-12, doi: 10.1360/N012016-00150. pdf file

7. Large-time behavior for fluid and kinetic plasmas with collisions, *Bulletin
of the Brazilian Mathematical Society. New Series.* 47 (2016), no. 1, 307-321.
pdf file

8. With Shuangqian Liu and Jiang Xu: Global well-posedness in spatially
critical Besov space for the Boltzmann equation, *Archive for Rational
Mechanics and Analysis*, 220 (2016), no. 2, 711-745. pdf file

9. With Shuangqian Liu, Haiyan Yin and Changjiang Zhu: Stability of the
rarefaction wave for a two-fluid plasma model with diffusion, *SCIENCE CHINA
Mathematics*, 59 (2016), no. 1, 67-84. pdf file

10. With Shuangqian Liu: Stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann
system, *SIAM Journal on Mathematical Analysis*, 47 (2015), no. 5, 3585-3647.
pdf
file

11. With Qingqing Liu and Changjiang Zhu: Darcy's law and diffusion for
a two-fluid Euler-Maxwell system with dissipation, *Mathematical Models and
Methods in Applied Sciences*, 25 (2015), 2089-2151. pdf file

12. With Shuangqian Liu: Time-periodic solutions of the Vlasov-Poisson-Fokker-Planck
system, *Acta Mathematica Scientia*, 35B (4) (2015), 876-886. pdf file

13. With Shuangqian Liu: Stability of rarefaction waves of the Navier-Stokes-Poisson
system, *J. Differential Equations*, 258 (2015), no. 7, 2495-2530. pdf file

14. With Zhaoyin Xiang: On the Cauchy problem for the two-component
Euler-Poincare equations, *Journal of Functional Analysis*, 267 (2014),
no. 8, 2698-2730. pdf file

15. Global smooth dynamics of a fully ionized plasma with long-range
collisions, *Annales de l'Institut Henri Poincare -Analyse non lineaire*,
31 (2014), no. 4, 751-778. pdf file

16. With Shuangqian Liu: Cauchy problem on the Vlasov-Fokker-Planck
equation coupled with the compressible Euler equations through the friction
force, *Kinetic and Related Models*, 6 (2013), no. 4, 687-700. pdf file

17. With Shuangqian Liu: The Vlasov-Poisson-Boltzmann system without
angular cutoff, *Communications in Mathematical Physics*, 324 (2013), no.
1, 1-45. pdf file

18. With T. Yang and H.-J. Zhao: The Vlasov-Poisson-Boltzmann system for
soft potentials, *Mathematical Models and Methods in Applied Sciences*, 23 (2013), no. 6, 979-1028. pdf
file

19. With Shuangqian Liu, Tong Yang and Hui-Jiang Zhao: Stability of the
nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff
potentials, *Kinetic and Related Models*, 6 (2013), no. 1, 159-204. pdf file

20. With Xiongfeng Yang: Stability of rarefaction wave and boundary
layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations, *Communications
on Pure and Applied Analysis*, 12 (2013), no. 2, 985-1014. pdf
file

21. With Zhaoyin Xiang: A note on global existence for the chemotaxis-Stokes
model with nonlinear diffusion, *International Mathematics Research Notices*,
(2012). doi: 10.1093/imrn/rns270. pdf file

22. With W.-X. Li: Hypocoercivity for the linear Boltzmann equation with
confining forces, *Journal of Statistical Physics*, 148 (2012), no. 2, 306-324. pdf
file

23. With Y. Ueda and S. Kawashima: Decay structure for symmetric
hyperbolic systems with non-symmetric relaxation and its application, *Archive
for Rational Mechanics and Analysis*, 205 (2012), no. 1, 239-266. pdf
file

24. With L. Ruan and C.-J. Zhu: Optimal decay rates to conservation laws
with diffusion-type terms of regularity-gain and regularity-loss, *Mathematical
Models and Methods in Applied Sciences*, 22 (2012), no. 7, 1250012 (39
pages). pdf
file

25. With T. Yang and H.-J. Zhao: The Vlasov-Poisson-Boltzmann system in
the whole space: the hard potential case, *Journal of Differential Equations*,
252 (2012), no. 12, 6356-6386. pdf
file

26. Green's function and large time behavior of the
Navier-Stokes-Maxwell system, *Analysis and Applications*, 10 (2012),
no. 2, 133-197. pdf
file

27. With Q.Q. Liu and C.-J. Zhu: The Cauchy problem on the compressible
two-fluids Euler-Maxwell equations, *SIAM Journal on Mathematical Analysis*,
44 (2012), no. 1, 102-133. pdf
file

28. Dissipative property of the Vlasov-Maxwell-Boltzmann system with a
uniform ionic background, *SIAM Journal on Mathematical Analysis*, 43 (2011),
no. 6, 2732-2757. pdf
file

29. With R.M. Strain: Optimal large-time behavior of the
Vlasov-Maxwell-Boltzmann system in the whole space, *Communications on Pure
and Applied Mathematics*, 64 (2011), no. 11, 1497-1546. pdf
file

30. Global smooth flows for the compressible Euler-Maxwell system:
Relaxation case, *Journal of Hyperbolic Differential Equations*, 8 (2011),
no. 2, 375-413. pdf file

31. Hypocoercivity of the linearized dissipative kinetic equations, *Nonlinearity*,
24 (2011), no. 8, 2165-2189. pdf
file

32. With J. Carrillo and A. Moussa: Global classical solutions close to
equilibrium to the Vlasov-Euler-Fokker-Planck system, *Kinetic and Related
Models*, 4 (2011), no. 1, 227-258. pdf file

33. With R.M. Strain: Optimal time decay of the Vlasov-Poisson-Boltzmann
system in $R^3$, *Archive for Rational Mechanics and *Analysis, 199
(2010), no. 1, 291-328. pdf file

34. With M. Fornasier and G. Toscani: A kinetic flocking model with
diffusions, *Communications in Mathematical Physics*, 300 (2010), no. 1,
95-145. pdf file

35. With A. Lorz and P. Markowich: Global Solutions to the coupled
chemotaxis-fluid equations, *Communications in Partial Differential Equations*,
35 (2010), no. 9, 1635-1673. pdf file

36. With K. Fellner and C.-J. Zhu: Energy method for multi-dimensional
balance laws with non-local dissipation, *Journal Mathematiques Pures
Appliquees*, 93 (2010), no. 6, 572-598. pdf file

37. With T. Yang: Stability of the one-species Vlasov-Poisson-Boltzmann
system, *SIAM Journal on Mathematical Analysis*, 41 (2010), no. 6,
2353-2387. pdf file

38. Stability of the Boltzmann equation with potential forces on torus, *Physica
D: Nonlinear Phenomena* 238 (2009), 1808-1820. pdf file

39. With H.-F. Ma: Global existence and convergence rates for the 3-D
compressible Navier-Stokes equations without heat conductivity, *Indiana
University Mathematics Journal *57 (2008), 2299-2320. pdf file

40. With M.-R. Li and T. Yang: Propagation of singularities in the
solutions to the Boltzmann equation near equilibrium,* Mathematical Models
and Methods in Applied Sciences* 18 (2008), no. 7, 1093-1114. pdf file

41. On the Cauchy problem for the Boltzmann equation in the whole space:
Global existence and uniform stability in $L^2_\xi(H^N_x)$, *Journal of
Differential Equations* 244 (2008), no. 12, 3204-3234. pdf file

42. With S. Ukai, T. Yang and H.-J. Zhao: Optimal decay estimates on the
linearized Boltzmann equation with time-dependent forces and their
applications, *Communications in Mathematical Physics* 277 (2008), no. 1,
189-236. pdf file

43. With H.-X. Liu, S. Ukai and T. Yang: Optimal $L^p$-$L^q$ Convergence
rates for the Navier-Stokes equations with potential force, *Journal of
Differential Equations* 238 (2007), no. 1, 220-233. pdf file

44. With S. Ukai, T. Yang and H.-J. Zhao: Optimal convergence rates for
the compressible Navier-Stokes equations with potential forces, *Mathematical
Models and Methods in Applied Sciences* 17 (2007), No. 5, 737-758. pdf file

45. With S.-P. Lin and C.J. Zhu: Optimal $L^p$ ($1\leq p \leq \infty$) rates
of decay to linear diffusion waves for nonlinear evolution equations with
ellipticity and dissipation, *Nonlinear Analysis: Theory, Methods &
Applications* 66 (2007), no. 11, 2335-2344. pdf file

46. With T. Yang and C.-J. Zhu: Navier-Stokes equations with degenerate
viscosity, vacuum and gravitational force, *Mathematical Methods in the
Applied Sciences* 30 (2007), no. 3, 347-374. pdf file

47. With T. Yang and C.-J. Zhu: Existence of stationary solutions to the
Vlasov-Poisson-Boltzmann system, *Journal of Mathematical Analysis and
Applications* 327 (2007), no. 1, 425-434. pdf file

48. With S.-Q. Tang and C.-J. Zhu: Asymptotics in nonlinear evolution
system with dissipation and ellipticity on quadrant, *Journal of Mathematical
Analysis and Applications* 323 (2006), no. 2, 1152-1170. pdf file

49. With M. Zhang and C.-J. Zhu: $L^1$ stability for the
Vlasov-Poisson-Boltzmann system around vacuum, *Mathematical Models and
Methods in Applied Sciences* 16 (2006), No. 9, 1505-1526. pdf
file

50. With T. Yang and C.-J. Zhu: $L^1$ and BV-type stability of the
Botlzmann equation with external forces, *Journal of Differential Equations*
227 (2006), no. 1, 1-28. pdf file

51. With T. Yang and C.-J. Zhu: Boltzmann equation with external force
and Vlasov-Poisson-Boltzmann system in infinite vacuum, *Discrete and
Continuous Dynamical Systems* 16 (2006), no. 1, 253-277. pdf file

52. With T. Yang and C.-J. Zhu: Global existence to Boltzmann equation
with external force in infinite vacuum, *Journal of Mathematical Physics*
46 (2005), 053307, 13pp. pdf file

53. With C.-J. Zhu: Asymptotics of dissipative nonlinear evolution
equations with ellipticity: different end states, *Journal of Mathematical
Analysis and Applications* 303 (2005), no. 1, 15-35.

54. With C.-J. Zhu: A note on semiconcave function, *Applicable
Analysis* 82 (2003), no. 9, 889-894.

55. With C.-J. Zhu: Existence and uniqueness of entropy solution to
initial boundary value problem for the inviscid Burgers equation, *Journal of
Physics. A.* 36 (2003), no. 8, 2099-2107.

**Conference Papers
and Short Surveys **

1. With Shuichi Kawashima and Yoshihiro Ueda: Dissipative structure of
the coupled kinetic-fluid models, *Nonlinear Dynamics in Partial Differential
Equations*, Edited by S.-I. Ei, S. Kawashima, M. Kimura and T. Mizumachi.
Advanced Studies in Pure Mathematics, 64 (2015), 327-335.

2. Asymptotic stability of kinetic plasmas for general collision
potentials, Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona, A.
Bressan, P. Marcati and A. Marson (Editors), *AIMS on Applied Mathematics*,
8 (2014), 533-540.

3. With R.M. Strain: On the full dissipative property of the Vlasov-Poisson-Boltzmann
system, Hyperbolic Problems: Theory, Numerics and Applications, *Series in
Contemporary Applied Mathematics CAM*, 18 (2012), no. 2, 398-405. pdf
file

4. With S. Ukai and T. Yang: A combination of energy method and
spectral analysis for studies on systems for gas motions, *Frontiers of
Mathematics in China* 4 (2009), no. 2, 253-282. pdf file

5. The Boltzmann equation near equilibrium states in $R^n$, *Methods
and Applications of Analysis* 14 (2007), No. 3, 227-250. pdf file

Title: Some Mathematical Theories on the Gas Motion Under the
Influence of External Forcing** **pdf file

*Note: Most of
the information in the thesis has been published in the form of research
papers.*

1. Lectures in AMSS, CAS, August 21-25, 2017. Part II and Part III.

2. Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics, May 27-29, 2016, Kyoto University, Kyoto, Japan. pdf file

3. Session on Qualitative behavior of PDEs in fluid mechanics and related topics, The 10th International Society for Analysis, its Applications and Computation, August 3-8, 2015, University of Macau, Macao. pdf file

4. Workshop on Kinetic and Related Equations, July 5-10, 2015, The Casa Matematica Oaxaca (CMO), Oaxaca, Mexico. pdf file

5. XV International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2014), Jul. 28 - Aug. 1, 2014, IMPA, Rio de Janeiro, Brazil. pdf file

6. The Sixth International Congress of Chinese Mathematicians (ICCM), July 14-19, 2013, Taipei. pdf file

7. The Fourteenth International Conference on Hyperbolic Problems: Theory Numerics and Applications, Jun. 25-29, 2012, University of Padova, Italy. pdf file

8. Conference on Kinetic Theory and Related Fields, Jun. 22-24, 2011, Pohang University of Science and Technology, Korea. pdf file

9. Austrian-Chinese Workshop on Dissipative Systems: Kinetic Theory and Semiconductor Applications, Nov. 3-5, 2010, Vienna University of Technology, Austria. pdf file

10. Workshop on Kinetic and Related Models, Oct. 15-19, 2010, Northwest University, China. pdf file

11. Concentration en vitesse et en espace dans les modeles cinetiques et diffusifs (chemotaxis, gravitation, swarming), Oct. 6-7, 2009, IHP and ENS, Paris. pdf file

12. Modern Topics in Nonlinear Kinetic Equations, Apr. 20-22, 2009, University of Cambridge, UK. pdf file

13. Twelfth International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Jun. 9-13, 2008, University of Maryland, USA. pdf file

14. International Conference on Conservation Laws & Kinetic equations, Dec. 7-12, 2006, Shanghai Jiao Tong University, China. pdf file

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