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
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 1265574, July 1, 2013-June 30, 2016.
- 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 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