Course Information
Instructor  Dr. Changhui Tan 
Lectures  Tu Th 9:25am  10:40am, at HBH 227 
Office  HBH 426 
Office Hours  M 2:00pm  4:00pm, or by appointment 
Textbooks  There are no required textbooks. 
References  Lawrence C. Evans, Partial Differential Equations: Second Edition, Graduate Studies in Mathematics 19, 2010. (ISBN: 9780821849743) 
Andrew J. Majda and Andrea L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics 27, 2001. (ISBN: 9780521639484) 
Course Description
 We aim to cover the mathematical theories for three important topics in partial differential equations. A brief outline is as follows:

 Second order elliptic equations:
 Laplace equation.
 Sobolev spaces, embedding, interpolation.
 Weak solutions, LaxMilgram theorem, regularity.  Second order parabolic equations:
 Heat equation.
 Weak solutions, maximum principle.
 Semigroup theory, application on the NavierStokes equations.  The incompressible Euler equations:
 Vorticitystream formulation, method of characteristics.
 2D Euler: global wellposedness, fast growth in vorticity gradient.
 3D Euler: possible blowup scenarios.
 Second order elliptic equations:
Grades
 The grade will be based on class participation, occational homework assignments, as well as a possible final project.
Contact Information
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