Assistant Professor Chi-Hin Chan

Contact

• Email: cchan@math.nctu.edu.tw
• Tel: 03-571-2121 ext. 56464
• Fax: 03-572-4679
• Address: Department of Applied Mathematics, National Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30010, ROC

Teaching

• Fall Semester, 2012：
  • Partial Differential Equations (I)
• Spring Semester, 2013：
  • Partial Differential Equations (II)
  • Discrete Mathematics

Vitae

• Education
  • University of Texas at Austin, Ph.D. in Mathematics , May 2008.
  • University of California at Berkeley, B.A. in Mathematics, May 2001.
• Research Areas
  • Analytic, geometric, and topological properties of solutions to incompressible Navier-Stokes equations on a Riemannian manifold.
  • Regularity of solutions to incompressible Navier-Stokes equations.
  • Regularity of solutions to P.D.E's with diffusion terms expressed by fractional Laplacian.
• Positions, Honors and Awards
  • Assistant Professor, Department of Applied Mathematics, National Chiao Tung University, Taiwan, starting form August 2012.
  • Postdoctoral fellow, The Institute of Mathematical Sciences (IMS) and the Department of Mathematics, Chinese University of Hong Kong, Fall 2011-Spring 2012.
  • Postdoctoral fellow, Institute for Mathematics and Its Applications (IMA), University of Minnesota, Minneapolis, Fall 2009-Spring 2011.
  • Lecturer, Department of Mathematics, University of Texas at Austin, Fall 2008-Spring 2009.
• Recent Research Projects
  The investigation of global properties of solutions to Navier-Stokes equation on a negatively curved
  manifold (101-2115-M-009-016-MY2)

Selected Publications

(A)   Refereed Papers：

1. Chi Hin Chan, Alex Vasseur. Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations. Methods Appl. Anal 14 (2007), no. 2, 197-212.
2. Chi Hin Chan. Smoothness Criteria for Navier-Stokes equations in terrms of regularity along the streamlines. Method Appl. Anal. 17 (2010), no. 1, 081-104.
3. Chi Hin Chan, Magdalena Czubak. Regularity of solutions for the critical N-dimensional Burgers' equation.
4. Chi Hin Chan, Magdalena Czubak, and Luis Silvestre. Eventual regularization of the slightly supercritical fractional Burgers equation. Discrete Contin. Dyn. Syst., 27(2):847-861, 2010.
5. Luis Caffarelli, Chi Hin Chan, Alexis Vasseur. Regularity theory for parabolic nonlinear integral operators. J. Amer. Math. Soc. 24 (2011), no. 3, 849869.
6. Chi Hin Chan, Magdalena Czubak. Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting. To appear in Dynamics of P.D.E.
7. Chi Hin Chan, Tsuyoshi Yoneda. On possible isolated blow-up phenomena and regularity criterion of the 3D Navier-Stokes equation along the streamlines. Method and Applications of Analysis. Vol.19, No.3 pp.211-242, September 2012.
8. Chi Hin Chan, Tsuyoshi Yoneda. On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space. ArXir e-prints, Feb 2013.

(B)   Conference Papers：

1. Nonuniqueness of Leray-Hopf type solutions to the Navier-Stokes equation on 2 dimensional hyperbolic manifolds. Invited talk in the conference Workshop on Applied Analysis and Applied PDEs. University of Vicroria, July 12-July 15, 2011.
2. Regularity theory for nonlinear integral operators. Invited talk in the conference Nonlocal operators and partial differential equations Bedlewo, June 27-July 3, 2010.
3. Invited talk in the Special Session on Partial Differential Equations from Fluid Mechanics at the AMS Fall Southeastern Meeting in Boca Raton, FL, Oct 30-Nov 1, 2009.
4. Invited talk in the Special Session on Nonlinear partial differential equations and applications at the AMS Spring Centeral Sectional Meeting in Urbana, IL, March 27-29, 2009.

(C)   Dissertation：

1. Chi Hin Chan. The De Giorgi's Method as Applied to The Regularity Theory for Incompressible Navier Stokes Equations. Ph.D. thesis submitted to the graduate school of UT Austin. Thesis Advisor: Professor Alexis Vasseur.

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