Welcome to Changyou Wang's homepage
Position
Education
- Ph.D: Department of Mathematics,
Rice University. May 1996
Ph.D. advisor: Robert M. Hardt,
W. L. Moody Professor of Mathematics.
- M.S.: Institute of Mathematics, Academia Sinica, P.R. China. May 1992
M.S. advisor: Professor WeiYue Ding.
- B.S.: Department of Mathematics, Beijing Normal University. July 1989.
Contact Information
Department of Mathematics
Purdue University
150 N. University Street
West Lafayette, IN 47907-2067
Phone: (765) 49-42719
Fax: (765) 49-40548
Email: wang2482@purdue.edu
Office: MATH 714
Research Interests
Partial Differential Equations
Calculus of Variations
Geometrical Analysis
Application of Geometry Measure Theory
PDE SEMINARS
Honors and Awards
- Alfred P. Sloan Dissertation Fellowship, 1995-1996.
- American Mathematical Society Centennial Fellowship, 1999-2000.
- IMA New Directions Research Professorship, 2009-2010.
- Simons Fellowship in Mathematics, 2012-2013.
Grant Supports
- NSF DMS 2101224, July 1, 2021-June 30, 2024.
- NSF DMS 1764417, July 1, 2018-June 30, 2022.
- NSF DMS 1265574, July 1, 2013-June 30, 2017.
- NSF DMS 1001115, August 1, 2010-July, 31, 2013.
- NSF DMS 0601162, July 1, 2006-June 30, 2010.
- NSF-NSFC CMR 0819742, July, 1 2008-June 30, 2011.
- NSF DMS 0400718, July 1, 2004-June 30 2007.
- NSF DMS 9972043, August 1, 1999-July 31, 2002 (Co-PI, R. Jensen and N. Barron=PI).
- NSF DMS 9970549, August 1, 1999-July 31, 2002.
- NSF DMS 9706855, August 1, 1997-July 31, 1999.
List of Publications
Professional Services
A Family Picture
Some Previous Conferences
- 63th Midwest PDE seminar, November 7-8, 2009, Purdue University.
- Iowa PDE workshop, April 30-May 2, 2010, University of Iowa.
- International Conference on Geometric Nonlinear PDEs, June 14-18, 2010,
Beijing International Center for Mathematics Research, Beijing, China.
- Mini-workshop on Geometric Analysis, June 23-24, 2010, University of Warwick, England.
- Workshop on Geometric Analysis, July 5-9, 2010, East China Normal University, Shanghai, P.R. China.
- The Second Oklahoma PDE Workshop,
October 9-10, 2010, University of Oklahoma.
- International Conference on Partial Differential Equations in Fluid Mechanics and Material Sciences,
Jan. 8-10, 2011, South China Normal Univ., Guangzhou, P.R. China.
- International Confernece on Recent Developments in L-infinity Variational
Problems and Associated Nonlinear Partial Differential Equations
- Second Ohio River Analysis Meeting, April 21-22, 2012
Current Teachings at Purdue University
Spring 2023
Fall 2022
Spring 2022
Fall 2020
Spring 2020
Fall 2019
Fall 2018
Spring 2018
Fall 2017
Spring 2017
Fall 2016
Fall 2015
Fall 2014
Spring 2015
Some Courses Taught at University of Kentucky
Analysis/PDE Seminars Organized at University of Kentucky
Recent Publications
(The research
reported in the following papers is supported by NSF grants
DMS 0400718, DMS 0601162, DMS 1001115, DMS 1265574)
- Stable stationary harmonic maps into spheres.
Acta Math. Sinica (Engl. Ser.) 22 (2006), no. 2, 319-330
(with FangHua Lin). pdf file.
- On Landau-Lifshitz equation in dimensions at most four.
Indiana Univ. Math. J. Vol. 55, no.6 (2006) 1615-1644.
dvi file.
- Generalized cone comparison principle for viscosity solutions of
the Aronsson equation and absolute minimizers. Comm. P.D.E. V. 31, No.
7 (2006) 1027-1046 (with R. Gariepy, Y. Yu). dvi file
.
- The Aronsson equation for absolute minimizers of $L^\infty$
functionals associated with vector fields satisfying H\"ormander's
conditions. Trans. AMS. 359 (2007), 91-113.
dvi file.
- Heat flow of biharmonic maps in dimension four and its
application. Pure and Applied Math. Quarterly, Vol. 3, No. 2 (2007)
595-613 (Special issue: In honor of L. Simon, Part 1 of 2). pdf file.
- Finite time singularity of the Landau-Lifshitz-Gilbert equation.
Int. Math. Reas. Notices, Vol. 2007 (with Shijin Ding). pdf file
- Asymptotic behavior of infinity harmonic functions near an
isolated singularity. Int. Math.
Reas. Notices, Vol. 2008, article ID rnm163, 23 pages (with O. Savin,
Y. Yu). pdf file .
- Heat flow of harmonic maps whose gradients belong to
$L^n_xL^\infty_t$. Arch. Rational Mech. Anal. 188 (2008), 309-349.
pdf file
- Harmonic maps from manifolds of $L^\infty$-Riemannian metrics.
Calc. Var. & PDE (2008), Vol 32, 387-405 (with W. Ishizuka). pdf
file .
- $C^1$-regularity of the Aronsson equation in $\R^2$,
Annales I'Institut H. Poincar\'e- Analyse non lin\'eaire, 25 (2008) 659-678
(with Y. Yu). dvi file .
- Uniqueness and nonuniqueness of viscosity solutions to Aronsson's
equation. Arch. Ration Mech. Anal. (with
R. Jensen, Y. Yu), Vol. 190, no. 2 (2008) 347-370. pdf file .
- Derivation of the Aronsson equation for C-1 Hamiltonians.
Trans. AMS 361 (2009) 103-124(with M. Crandall, Y. Yu). pdf file .
- Aronsson's equation on Carnot-Carath\'eodory spaces.
Illinois Journal of Mathematics, Vol. 52, No. 3, Fall 2008, 757-772 (with Y. Yu). pdf
file .
- Boundary regularity for polyharmonic maps in the critical dimension.
Advances in Calculus of Variations 2, 2009, No. 1, 1-16(with T. Lamm).
pdf file .
- Regularity of Dirac-harmonic maps.
Int. Math. Reas. Notices, 2009, no. 20, 3759-3792 (with D. L. Xu).
pdf file .
- Landau-Lifshitz-Maxwell equation in dimension three.
Pacific J. Math., Vol. 243, No. 2, 2009, 243-276(with S.J. Ding, X.G. Liu).
pdf file .
- Liquid crystall flows in two dimensions.
Arch. Ration. Mech. Anal., 197 (2010) 297-336 (with F. H. Lin, J. Y. Lin)
pdf file .
- Notes on the regularity of harmonic map systems.
Proceedings of American Mathematical Society, 138 (2010) no. 6, 2015-2023 (with T. Huang)
pdf file .
- A Remark on Nonlinear Dirac Equations.
Proceedings of American Mathematical Society, 138 (2010), 3753-3758.
pdf file .
- Weak solution to compressible hydrodynamic flow of liquid crystals in 1D.
DCDS-B,15 (2011), no. 2, 357-371(with S. J. Ding, Y. H. Wen).
pdf file .
- Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data.
Arch. Ration. Mech. Anal., 200 (2011), no. 1, 1-19. pdf file .
- On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals.
Chinese Annals of Mathematics, Ser. B 31 (2010), no. 6, 921-938(with F. H. Lin). pdf file .
- Well-posedness for the heat flow of polyharmonic maps with rough initial data.
Advances in Calculus of Variations, 4 (2011), no. 2, 175-193. (with T. Huang).
pdf file .
- On the heat flow of equation of surfaces of constant mean curvature.
Manuscripta Math., 134 (2011), no. 1-2, 259-271 (with T. Huang, Z. Tan). pdf file .
- Well-posedness for the heat flow of biharmonic maps with rough initial data.
J. Geom. Anal., 22 (2012), no. 1, 223-243. pdf file .
- Compressible hydrodynamic flow of liquid crystals in 1D.
DCDS-A, 32 (2012), no. 2, 539-563(with S. J. Ding, J. Y. Lin, Y. H. Wen). pdf file .
- Phase transitions for potentials of high dimensional wells.
CPAM, 65 (2012), no. 6, 833-888 (with F. Lin, and X. Pan). pdf file .
- Strong solutions of the compressible nematic liquid crystal flow.
JDE, 252 (2012), no. 3, 2222-2265 (with T. Huang, H. Y. Wen). pdf file .
- Boundary regularity of stationary biharmonic maps. CVPDE, 45 (2012), no. 1-2, 165-191
(with Huajun Gong, Tobias Lamm). pdf file .
- Blow up criterion for compressible nematic liquid crystal flows in dimension three.
ARMA, 204 (2012), no. 1, 285-311(with T. Huang, H. Y. Wen). pdf file .
- Blow up criterion for nematic liquid crystal flows,
CPDE, 37 (2012), no. 5, 875-884 (with T. Huang). pdf file .
- Energy identity for a class of approximate biharmonic maps into sphere in dimension four, DCDS-A, 33 (2013), no. 2, 861-878
(with Shenzhou Zheng).arXiv:1110.6536 pdf file .
- Energy identity for approximate biharmonic maps to Riemannian manifolds and its application, Journal of Functional Analysis, 263 (2012), no. 4, 960-987
(with Shenzhou Zheng). arXiv:1112.6362 pdf file .
- $C^1$-boundary regularity of planar infinity harmonic functions, Math. Res. Lett., 19 (2012), no. 4, 823-835(with Yifeng Yu).
pdf file .
- Well-posedness of nematic liquid crystal flow in
$L^3_uloc(R^3)$, Arch. Ration. Mech. Anal, 210 (2013), no.1, 177-218 (with J. Hineman) pdf file .
- Harmonic maps on domains with piecewise Lipschitz continuous metrics. Pacific J. Math., 264 (2013), no.1, 125-149
(with Haigang Li). pdf file .
- Regularity and uniqueness of the heat flow of biharmonic maps. CVPDE, 50 (2014), no. 3-4, 491-524 (with J. Hineman, T. Huang).
pdf file .
- On the rigidity of nematic liquid crystal flow on $S^2$. J. Funct. Anal., 266 (2014), no. 8, 5360-5376 (with Xiang Xu)
pdf file .
- Regularity and existence of global solutions to the Ericksen-Leslie system in $R^2$. Comm. Math. Phys., 331 (2014), no. 2, 805-850
(with J. R. Huang, F. H. Lin).
pdf file .
- Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
(with Fanghua Lin), Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014), no. 2029, 20130361, 18 pp. pdf file.
- Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey speace (with J. Y. Lin, B. S. Lai), CVPDE, 54 (2015), no. 1, 665-692,
pdf file .
- Global existence of weak solutions of the nematic liquid crystal flow in dimension
three (with Fanghua Lin), CPAM, 69 (2016), no. 8, 1532-1571 pdf file.
- MULTIPLE VALUED MAPS INTO A SEPARABLE HILBERT
SPACE THAT ALMOST MINIMIZE THEIR p DIRICHLET
ENERGY OR ARE SQUEEZE AND SQUASH STATIONARY
(with PHILIPPE BOUAFIA, THIERRY DE PAUW), CVPDE, 54 (2015), no. 2, 2167-2196.pdf file .
- On uniqueness of heat flow of harmonic maps (with T. Huang), IUMJ, Vol. 65, No. 5 (2016), 1525-1546.
pdf file.
- Global finite energy weak solutions to the compressible nematic
liquid crystal flow in dimension three (with Junyu Lin and Baishun Lai), SIAM Jour. Math. Anal. 47 (2015), no. 4, 2952-2983. pdf file.
- Everywhere differentiability of viscosity solutions to a class of Aronsson's equations
(with Juhana Siljander and Yuan Zhou), Annales IHP-ANL 34 (2017), no. 1, 119-138 pdf file.
- Finite time singularity of the nematic liquid crystal flow in dimension three (with Tao Huang, Fanghua Lin, and Chun Liu), ARMA, 221(3) (2016), 1223-1254.
pdf file.
- Heat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary (with T. Huang, L. Liu, and Yong Luo), J. Elliptic and Parabolic Equations, Vol 2 (2016), 1-26,
pdf file.
- Uniqueness of absolute minimizers for L-infinity functionals involving Hamiltonians H(x,p) (with Qianyun Miao, Yuan Zhou), ARMA, 223 (2017), no. 1, 141-198 pdf file.
- Weak solutions of geometric flows associated to integro-differential harmonic maps (with Armin Scikorra, Yannick Sire), Manuscripta Math., in press,
pdf file.
- Forward self-similar solutions to the viscoelastic Navier-Stokes equation with damping (with B. S. Lai, J. Y. Lin), SIAM J. Math. Anal., 49 (2017), no. 1, 501-529.
pdf file.
- Remarks on approximate harmonic maps in dimension two, CVPDE, 56 (2017), no. 2, 56:23.pdf file.
- Heat flow of Yang-Mills-Higgs functionals in dimension two (with C. Song), Journal of Functional Analysis, in press pdf file.
- Boundary bubbling analysis of approximate harmonic maps under either weak or strong anchoring conditions in dimension two (with T. Huang), IMRN, to appearpdf file.
Recent Preprints
- Partial regularity of suitable weak solutions to the liquid crystal flow in three dimensions.
In preparation (with F. H. Lin).
- Boundary regularity for a new class of minimizing harmonic maps. In preparation (with F. H. Lin).
Monography and Lecture Notes
- The Analysis of Harmonic Maps and Their Heat Flows, 267 pages
(with F. H. Lin), by World Scientific Publisher Inc, ISBN-109812779523.
- An Introduction of Infinity Harmonic Functions.
Preprint, 2008. pdf file .
- Lecture note of the Naiver-Stokes equation.
pdf file .
- An open question on regularity of Aronsson's equation.
Communications in Mathematical Analysis, Proceeding of the 2006 Midwest Geometry
Conference, pp. 80-83 (2008), edited by E. B. Lin, W. Wei.
pdf file