Associate Professor Chi-Hin Chan

Contact

• Email: cchan@math.nctu.edu.tw
• Tel: 03-571-2121 ext. 56464
• Fax: +886-03-572-4679
• Address: Department of Applied Mathematics, National Yang Ming Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30010, ROC

Teaching

• Fall Semester, 2024：
  • Introduction to Analysis (I), Honor Class
  • General Topology
• Spring Semester, 2025：
  • Introduction to Analysis (II), Honor Class
  • The use of differential forms in algebraic topology

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, Alexis F. 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. Ann. Tnst. H. Poincare Anal. Non Lineaire. 27(2): 471-501,2010.
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 F. 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. Dynamics of PDE, Vol 10, No1, 43-77, 2013.
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.Dynamics of PDE, Vol 10, No 3, 209-254, 2013.
9. Chi Hin Chan, Magdalena Czubak. Remarks on the weak Formulation of the Navier- Stoker equations on the  2D hyperbolic space. Accepted for publication in Ann. Inst. H. Poincare Anal.Non Lineaire.
10. Chi Hin Chan, Magdalena Czubak. Tsuyoshi Yoneda. An ODE for boundary layer separation on a sphere and a hyperbolic space. Phys. D 282 (2014), 34-38. 
11. Chi Hin Chan, Alexis F. Vasseur. De Giorgi techniques applied to the Holder regularity of solutions to Hamilton- Jacobi equations. ArXiv e-print, November 2014.
12. Chi Hin Chan, Magdalena Czubak. Liouville Theorems for The Stationary Navier Stokes Equation On a Hyperbolic Space. ArXiv e-print January 2015.
13. Chi Hin Chan, Che-Kai Chen, Magdalena Czubak, Asymptotic behavior of the steady Navier-Stokes equation on the hyperbolic plane, accepted for publication in Dynamics of P.D.E.
14. Chi Hin Chan, Magdalena Czubak, Marcelo M. Disconzi. The formulation of the Navier- Stokes equations on Riemannian manifolds, Journal of Geometry and Physics 121(2017) 335-346.
15. Chi Hin Chan,  Magdalena Czubak,  Antithesis of the Stokes paradox on the hyperbolic plane. ArXiv e-print, August, 2017

(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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