Position: Research
Scientist in Partial Differential Equation
Email: renjun.duan@oeaw.ac.at
Tel.: +43-732-24685250
Fax:
+43-732-24685212
Address:
Johann Radon Institute for Computational and Applied
Mathematics (RICAM)
Altenbergerstrasse 69, A-4040 Linz, Austria
Curriculum
Vitae (full) pdf file
Note: I am moving to The Chinese University of Hong
Kong. Here
is my new contact information.
Educations
--PhD, Sep. 2005-Aug. 2008, City University of Hong Kong, Hong Kong
--MSc, Sep. 2002-Jul. 2005, Huazhong Normal University, China
Research Interests
I am interested in the theoretical study of partial differential
equations arising from Mathematical Physics and Biology such as fluid dynamics,
kinetic theory and chemotaxis. Research topics include the Boltzmann equation,
Navier-Stokes equations and mixed-type equations with relaxation. By using
tools from PDE and Functional Analysis, I try to understand well-posedness and large-time
behavior for the Cauchy problem or initial boundary value problem.
Academic Visits
--City University of Hong Kong, HK, Dec. 1-31, 2009
--University of Cambridge, UK, Oct. 26-Nov. 22, 2009
--Universitat Autonoma de Barcelona, Spain, Oct. 19-24, 2009
--University of Pavia, Italy, May 24-30, 2009.
--University of Cambridge, UK, Nov. 3-10, 2008.
--Universite de Rouen, France, Feb. 4-8, 2008.
--Institut de Recherche de l'Ecole navale, France, Jan. 7-Feb. 3, 2008.
--National Taiwan University, Taiwan, Jun. 15-Jul. 15, 2007.
Selected talks
--Concentration en vitesse et en espace dans les modèles cinétiques et
diffusifs (chemotaxis, gravitation, swarming), Oct. 6-7, 2009, IHP and ENS,
Paris. pdf file
--Modern Topics in Nonlinear Kinetic Equations, Apr. 20-22, 2009,
University of Cambridge, UK. pdf file
--Twelfth International Conference on “Hyperbolic Problems: Theory,
Numerics, Applications”, Jun. 9-13, 2008, University of Maryland, USA. pdf file
--International Conference on Conservation Laws & Kinetic equations,
Dec. 7-12, 2006, Shanghai Jiao Tong University, China. pdf file
Accepted and Published
Research Papers
1.
With A. Lorz and P. Markowich: Global Solutions to
the coupled chemotaxis-fluid equations, to appear in Communications in Partial Differential Equations (2010). pdf file
2.
With M. Fornasier and G. Toscani: A kinetic
flocking model with diffusions, to appear in Communications in Mathematical Physics (2010). pdf file
3.
With R.M. Strain: Optimal time decay of the
Vlasov-Poisson-Boltzmann system in R3, to appear in Archive for Rational Mechanics and Analysis (2010).
pdf file
4.
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
5.
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
6.
Stability of the Boltzmann equation with potential
forces on torus, Physica D: Nonlinear
Phenomena 238 (2009), 1808-1820. pdf file
7.
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
8.
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
9.
On the Cauchy problem for the Boltzmann equation in
the whole space: Global existence and uniform stability in L2_{\xi} (HN_x)$,
Journal of Differential Equations 244
(2008), no. 12, 3204-3234. pdf
file
10. 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
11. With H.-X. Liu,
S. Ukai and T. Yang: Optimal Lp-Lq Convergence rates for
the Navier-Stokes equations with potential force, Journal of Differential Equations 238 (2007), no. 1, 220-233. pdf file
12. 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
13. With S.-P. Lin
and C.J. Zhu: Optimal Lp (1≤p≤∞) 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
14. 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
15. 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
16. 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
17. With M. Zhang
and C.-J. Zhu: L1 stability for the Vlasov-Poisson-Boltzmann system
around vacuum, Mathematical Models and
Methods in Applied Sciences 16 (2006), No. 9, 1505-1526. pdf file
18. With T. Yang and
C.-J. Zhu: L1 and BV-type stability of the Botlzmann equation with
external forces, Journal of Differential
Equations 227 (2006), no. 1, 1-28. pdf file
19. 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
20. 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
21. 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.
22. With C.-J. Zhu:
A note on semiconcave function, Applicable
Analysis 82 (2003), no. 9, 889-894.
23. 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 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
2.
The Boltzmann equation near equilibrium states in Rn,
Methods and Applications of Analysis
14 (2007), No. 3, 227-250. pdf file
Submitted Papers
1.
Hypocoercivity of linear degenerately dissipative kinetic
equations, submitted preprint (Dec. 3, 2009). pdf
file, arXiv:0912.1733v1
2.
Global smooth flows for the compressible Euler-Maxwell
system: I. Relaxation case, submitted preprint (Jun. 10, 2010). pdf file, arXiv:1006.3606v1
3.
With Jose A. Carrillo and Ayman Moussa: Global
classical solutions close to equilibrium to the Vlasov-Euler-Fokker-Planck
system, submitted preprint (May 7, 2010). pdf file
4.
With Robert M. Strain: Optimal large-time behavior
of the Vlasov-Maxwell-Boltzmann system in the whole space, submitted preprint (Jun.
7, 2010). pdf file, arXiv:1006.3605v1
Work in Progress
1.
Global smooth flows for the compressible
Euler-Maxwell system: II. Non relaxation case.
2.
With Lizhi Ruan and Changjiang Zhu: On the Cauchy problem
of some conservation laws with diffusion-type terms.
3.
Dispersion of degenerately dissipative evolution
equations.
Note: Some information in
this part can change as time goes on.
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.
Last updated on July 26, 2010 by Renjun
Duan
