General Information
For a description of the course, including the grading policy, consult the course syllabus. Students are responsible for reading the syllabus and being aware of all the course and university policies.

There is no textbook for this course. Some references are suggested in the course syllabus.

Classes meet on TR, 1:15-2:30pm at Stevenson Center 1312.

Contact Information and Office Hours
Instructor's office: A1017, 17^th & Horton (Sony bld).
Instructor's email: marcelo.disconzi@vanderbilt.edu.
Instructor's office hours: Tuesdays, 4:10-6:10pm, Thursdays, 12-1pm, or by appointment.
Instructor's office phone: (615) 322-7147.

Schedule
Below is schedule for the course which will be updated as the course progresses (for the academic calendar, click here). HW will be posted on Brightspace.

Date	Material covered	Remarks
Aug 21	Introduction.
Aug 26	The relativistic Euler equations.
Aug 28	Characteristics of the relativistic Euler equations. Acoustical metric. Vorticity. Local well-posedness.
Sept 2	Irrotational flows. The Einstein-Euler system. Remarks on characteristic initial data.
Sept 4	The relativistic free-boundary Euler equations. Physical vacuum boundary condition.
Sept 9	No class. Make-up class to be scheduled.
Sept 11	No class. Make-up class to be scheduled.
Sept 16	Overview of the argument for LWP.
Sept 18	Good variables. Function spaces. Scaling analysis.
Sept 23	Energy estimates. Basic ideas. Function spaces.
Sept 25	Energy estimates.
Sept 30	Elliptic estimates. Overview of remaining arguments for LWP.
Oct 2	No class. Make-up class to be scheduled.
Oct 7	The Einstein-Euler system with a physical vacuum boundary.
Oct 9	Fall break, no class.
Oct 14	No class. Make-up class to be scheduled.
Oct 16	No class. Make-up class to be scheduled.
Oct 21	Discussion of key difficulties and main ideas.
Oct 23	Energy estimates: main argument.
Oct 28	Energy estimates: localization and analysis of error terms.
Oct 30	Elliptic estimates.
Nov 4	Time discretization: set up for LWP.
Nov 6	Details of the iteration scheme.
Nov 11	Convergence of the iteration scheme.
Nov 13	Regularization, the basics.
Nov 18	Regularization, self-adjointness.
Nov 20	Regularization, functional calculus.
Nov 25	Thanksgiving holidays, no class.
Nov 27	Thanksgiving holidays, no class.
Dec 2
Dec 4

Anonymous feedback
Students are encouraged to bring suggestions and discuss with the course instructor any concerns they may have, including something they think is not being properly handled in the course. But if you do not feel comfortable doing that, here you have the opportunity to send anonymous feedback.