Xinwei Yu, CAM Assistant Professor

Current Teaching (Spring 2008):

Curriculum Vitae:

• CAM Assistant Professor, Department of Mathematics, UCLA, USA, 2005 --
  
• Ph. D., Applied and Computational Mathematics, California Institute of Technology, USA, 2005.
• MS, Department of Scientific and Engineering Computations, School of Mathematical Sciences, Peking University, China, 2000
• BS, Department of Mathematics, Peking University, China, 1997

Full Curriculum Vitae

Research Interests:

• Singularity problems in fluid mechanics.
  

Journal Papers:

1. Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation, JMAA, 2008.
   
2. Level Set Dynamics and the non-blowup of the 2D quasi-geostrophic equation, Jian Deng, Thomas Y. Hou, Ruo Li and Xinwei Yu, Methods and Applications of Analysis, accepted, 2006.
   
3. A Level Set Formulation for the 3D Incompressible Euler Equations, Jian Deng, Thomas Y. Hou and Xinwei Yu, Methods and Applications of Analysis, 12(4): 427-440, Dec. 2005.
4. Improved Geometric Conditions for Non-blowup of the 3D Incompressible Euler Equation, Jian Deng, Thomas Y. Hou and Xinwei Yu, Comm. PDE., 31(2): 293-306, Jan. 2006.
5. Geometric Properties and Non-blowup of 3-D Incompressible Euler Flow, Jian Deng, Thomas Y. Hou and Xinwei Yu, Comm. PDE., 30(2): 225-243, Jan. 2005.
6. Singular Perturbation of a Class of Non-convex Functionals, Xinwei Yu, Zhiping Li and Lungan Ying, Nonlinear Analysis: Theory, Methods & Applications, Vol.52, 4, Feb.2003, pp.1129--1152.

Preprints:

• Note on the energy conservation of ideal MHD equations, in preparation.

Book Chapters:

1. Lecture Notes on Theory of Incompressible Inviscid Flow, Thomas Y. Hou and Xinwei Yu, to be published by Higher Education Press(Chinese) and World Scientific(English).

Invited Talks:

• 03/30/2008, Southern California Conference on the Mathematics of Fluids, USC; 02/13/2008, U. Alberta; 01/22/2008, U Colorado Boulder;
• 11/14/2007, UT Austin; 06/25/2007, Bedlewo.
• 04/30/2006, AMS sectional meeting, #1018, at San Francisco State University.
• 02/13/2006, Pennsilvania State University, PDE and Numerical Methods Seminar.
• 06/01/2005, University of california, Los Angeles, Applied Math Colloquim.
• 05/16/2005, California Institute of Technology, ACM Colloquim.
• 01/25/2005, University of California, San Diego, Computational and Applied Math Seminar.

Theses:

• Singular Perturbation of Non-convex Functionals and Microstructures with Surface Energy(in Chinese), Xinwei Yu, Master thesis, advised by Prof.Zhiping Li and Prof.Lungan Ying. School of Mathematical Science, Peking University, 2000. (.ps.gz file, 609K).
• Localized Non-blowup Conditions for 3D Incompressible Euler Flows and Related Equations, Xinwei Yu, Ph. D. thesis, advised by Prof. Thomas Y. Hou. Applied and Computational Mathematics, California Institute of Technology, 2005.

Teaching Experience (Most links to files are obsolete due to space limit)

1. Optimization: Math 164 (Fall 2005, Summer 2006, Winter 2007, Fall 2007)

2. Linear Algebra: Math 33A (Fall 2006), Math 115A (Spring 2006)

3. Teaching Experience @ Caltech