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Content of the course

Mathematical description of continua: Lagrangian and Eulerian coordinates, tensors, material derivative, conservation and constitutive laws. Stokes and Navier-Stokes equations: variational formulations and related functional spaces, boundary conditions, existence of solutions. Basic theory of compressible flows: Burgers equation, characteristics, shock waves. Introduction to Computational fluid dynamics.

Prerequisites:  The topics covered require notions from linear algebra, vectorial analysis, ODEs and/or PDEs. Some knowledge of abstract analysis is an asset.

Evaluation: Up to six assignments for a total of 60% and a final exam weighted 40% during the final exam period. The assignments might be presented and developed during the courses. The final exam will last three hours.

Lectures:  Monday, 10:00-11:30, KED 585 B005. Wednesday, 10:00-11:30, KED 585 B015.

Office hours: Monday and Wednesday, 11:30-13:00.

References:
1) Morton E. Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1981 (call number: QA 808.2 .G86 1981).
2) G. Duvaut, Mécanique des milieux continus, Masson, 1990 (call number: QA 808.2 .D89 1990).
3) Roger Temam, Navier-Stokes equations : theory and numerical analysis, Elsevier North-Holland, 1979 (call number: QA 374 .T44 1979).

Remarks:  If needed, any change in the course description will be announced in class. It is the responsability of the student to be aware of any modification of the course description. The web page of the course is available at https://mysite.science.uottawa.ca/ybourg/mat5187/mat5187.html

Follow the links to learn more about fluid dynamics

eFluids People, pictures, publications, almost everything on fluids.

Clay Mathematics Institute The official statement of the conjecture on Navier-Stokes equations

Yves Bourgault
Dept. of Mathematics and Statistics
room 203 C
585 King Edward
tel. 562-5800 ext 3506
e-mail: ybourg@mathstat.uottawa.ca
Link to my personal webpage