Eberly College of Science Mathematics Department

Math 505 - Spring 2018
              Mathematical Fluid Mechanics

NO CLASS TUESDAY JANUARY 10. Course will begin January 12, 2018.

ALL course content will be available on CANVAS.


Instructor:  Anna L. Mazzucato 

                    Office: 305 McAllister,  Office phone:  863-2036


                    Web page: (CANVAS)

                    Office hours (subject to change):  TUESDAY 5:00-6:30 PM

Please, email if you need to reach me outside of class or office hours.

Course meets TuTh 12:05PM - 1:20PM in McAllister Bldg 106.


PREREQUISITE: You must have successfully passed Math 402 or Math 404 or taken equivalent courses to register.



  • Attendance: 50% 
  • Final Oral Presentation: 50%

Grading will follow the Graduate School policies.

This course will provide an introduction to the mathematical modeling of fluid flow, specifically for incompressible fluids, using techniques from functional analysis and the analysis of partial differential equations.

Prerequisite are a solid background in Real Analysis, and a basic knowledge of Measure Theory and Functional Analysis. The syllabus is flexible and can be adapted to the students’ needs and interests.

Course topics:   

  1. Preliminaries: derivation of the Navier-stokes and Euler equations; vorticity equation, Kelvin circulation theorem; exact solutions.
  2. Viscous fluids: global-in-time existence of weak solutions and local-in-time exis- tence, uniqueness of strong solutions, energy estimates (possible additional topics: mild solutions and semigroups, partial regularity and self-similar solutions).

  3. Inviscid flows: existence by energy methods, vorticity-velocity formulation; global existence in 2 dimensions;

  4. Vanishing viscosity limit: boundary layers, Prandtl theory.

Additional topics if time allows : vortex sheets, patches, and rings; turbulence theories, dissipation of energy and enstrophy.


TEXTBOOKS (optional): 

Some items are active links to the e-book.


There will be a final project, consisting of a brief oral presentation on a topic agreed upon by the student and the instructor.


is required for this course. If you cannot attend class because of a valid excuse, such as illness or University-sponsored activity, please notify me. You are responsible for materials due and concepts covered. In particular, students will be expected to arrive before class start and leave only after class is over. I will make all efforts to start and finish class on time. Please, discuss any logistic problem with me.

Cell Phones must be turned off during all course activities. Please, clear with me beforehand use of computers, tablets, ect.

I WELCOME questions both during and outside class. ALL questions are very useful to both the instructor and the students. I also welcome general feedback about the course. Occasional changes in the syllabus or schedule will be announced in class and/or by email and/or available on the CANVAS Course Web Page.


ACADEMIC INTEGRITY: All Penn State policies regarding ethics and integrity apply to this course. For more information, see:

DISABILITIES: Penn State welcomes students with disabilities into the University’s educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814- 863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at

In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.

© Anna Mazzucato
Last modified: Mon Jan 1 07:17:17 EST 2018