|Topics in Partial Differential Equations|
|Time：||Wed. 15:10-17:00; Fri. 13:00-14:50|
|Instructor：||Dehua Wang [University of Pittsburgh]|
|Place：||Conference Room 1, Floor 1, Jin Chun Yuan West Building (近春园西楼1层第一会议室)|
This is an introductory course on analysis of partial differential equations arising in fluid mechanics and related areas. Possible topics include Euler equations and Navier‐Stokes equations of incompressible and compressible flows; existence, uniqueness, stability, regularity, singularities such as vortex sheets and shock waves; energy method, and Nash‐Moser method.
Connections with some problems in geometry may also be discussed. The course is self‐contained and is designed for the advanced undergraduate students and beginning graduate students.
Undergraduate partial differential equations
Reference for the course:
A. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics.
C. R. Doering, Applied Analysis of the Navier‐Stokes Equations.
G.‐Q. Chen and D. Wang, The Cauchy problem for the Euler equations compressible fluids.
E. Feireisl, Dynamics of Viscous Compressible Fluids.
R. S. Hamilton, The inverse function theorem of Nash and Moser.
Bulletin of the American Mathematical Society 7 (1982), 65–222.