MTH 627 Partial Differential Equations
Fall, 2011
Instructor: Elaine Cozzi
Office: KIDD 290
E-mail: [email protected]
Office Hours: Mon 10:00am-12:00pm, Wed 1:00pm-2:00pm
Course Location: STAG 411
Class Meetings: MWF 3:00-3:50 pm (3 credits)
Course Catalog Description: Advanced theory including existence proofs and
distributional approach.
Prerequisites: MTH 413 or MTH 513 or instructor consent.
Course Content: This course is an introduction to the mathematical theory of
incompressible fluid flow. We will study the Navier-Stokes equations (modeling
incompressible viscous fluid flow) and the Euler equations (modeling incompressible
inviscid fluid flow) in both two and three dimensions. Our approach will be primarily
theoretical, and we will rely on tools of advanced calculus and graduate level real
analysis.
The course will begin with an introduction to properties of the equations and of
important physical quantities associated with incompressible fluid flow (velocity,
vorticity, particle trajectory map). We will then derive and discuss the vorticity
formulations of the Euler and Navier-Stokes equations in two and three dimensions. We
will also study vortex dynamics of some interesting three-dimensional flows.
The remainder of the course will be devoted to existence and uniqueness theory for
solutions to the Navier-Stokes and Euler equations. We will focus on the theory for
classical solutions, but if time permits we will consider weak solutions as well.
Student Learning Outcomes:
Be able to state the Navier-Stokes and Euler equations and derive their corresponding
vorticity formulations.
Understand properties of the physical quantities associated with incompressible fluid
flow, such as the velocity, vorticity, and particle trajectory map.
Be able to prove statements on existence and uniqueness theory for the Navier-Stokes
and Euler equations.
Evaluation of Student Performance There will be a total of three problem sets used
to evaluate student performance. Problem sets will be posted on the course webpage at
least 10 days before their due date.
Learning Resources: Text: Vorticity and Incompressible Flow, by A. Majda and A.
Bertozzi (optional)
Statement Regarding Students with Disabilities:
"Accommodations are collaborative efforts between students, faculty and Disability Access
Services (DAS). Students with accommodations approved through DAS are responsible for
contacting the faculty member in charge of the course prior to or during the first week of the
term to discuss accommodations. Students who believe they are eligible for accommodations
but who have not yet obtained approval through DAS should contact DAS immediately at 541737-4098.”
Link to Statement of Expectations for Student Conduct:
http://oregonstate.edu/studentconduct/offenses-0
Diversity Statement: The College of Health and Human Sciences strives to create an
affirming climate for all students including underrepresented and marginalized
individuals and groups. Diversity encompasses differences in age, color, ethnicity,
national origin, gender, physical or mental ability, religion, socioeconomic background,
veteran status, sexual orientation, and marginalized groups. We believe diversity is the
synergy, connection, acceptance, and mutual learning fostered by the interaction of
different human characteristics.
Religious Holiday Statement:
Oregon State University strives to respect all religious practices. If you have religious
holidays that are in conflict with any of the requirements of this class, please see me
immediately so that we can make alternative arrangements.