Mathematics 283: Topics in Partial Differential Equations (Equations of Fluid Motion) (Fall 2003)
Instructor
Tom Beale
Description
The course will center on an analytical
understanding of the equations of fluid motion,
especially for incompressible flow, and of
numerical schemes used for fluid flow.
Part of the aim is to show how the analytical
tools learned in other courses can be used in
such a focused way. This will be
of value for advanced students in partial differential
equations, analysis, and applied math.
It is likely
that I will have each student present a fundamental
result or a recent paper, with the choice to be
worked out individually taking into account the
student's interests. Some possible topics:
basic results of existence and regularity for
the Navier-Stokes and Euler equations; fluid interfaces;
the projection method (a difference scheme for
viscous flow); vortex methods (or particle methods);
the immersed boundary method (for moving boundaries)
and related methods; computational methods for
singular integrals.
Prerequisites
Students should know the fundamentals of
Sobolev spaces and elliptic partial differential
equations (as in our Math 282) and functional analysis
(our Math 242, called Real Analysis II), as well as
basic topics in fluids (our Math 228 is plenty).
An interested student who has not had all of this
is welcome to talk to me about the appropriateness
of taking the course.
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