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


PhD Thesis

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.


Some talks

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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