Research Description for General Audience: Navier-Stokes Equation

In the chronological order from the most recent, modulus periodical revisions. The papers aside from the Manuscripts should be read with caution as they have not been thoroughly verified by any referee.

Manuscripts:

1.Remarks on the Method of Modulus of Continuity and the Modified Dissipative Porous Media Equation

http://arxiv.org/abs/0908.1257

Lecture Notes:

1. On the Method of Modulus of Continuity and Quasi-geostrophic Equation (Presented at Stanford University Student Geometric Analysis Seminar)

2. On the Global Regularity of the Logarithmically Supercritical Navier-Stokes Equation (Presented at Stanford University Student Geometric Analysis Seminar)

Personal Notes/Work in Progress:

1. A Remark on the Global Regularity of the Generalized MHD Equations

2. Global Existence and Uniqueness of a Modified Dissipative Critical Burgers Equation

3. Generalization of Kiselev and Nazarov's Program on the Supercritical QG

4. On the Global Regularity of the Critical Navier-Stokes Equation

5. On De Giorgi Type Method and Quasi-geostrophic Equation

6. Remarks on the Method of Modulus of Continuity and the Modified Dissipative Porous Media Equation Detailed Version

7. Global Regularity of a Modified Critical Dissipative Porous Media Equation

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