Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University
email: marcelo.disconzi at vanderbilt.edu
office: A1017, 17th & Horton (Sony bld)
phone: (615) 322 7147
mail to: 1326 Stevenson Center Ln, Vanderbilt University, Nashville, TN, 37240
Vanderbilt










Marcelo Mendes Disconzi
MATH 9100 - Seminar in analysis: relativistic free-boundary fluids

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, 17th & 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    
 Oct 23    
 Oct 28    
 Oct 30    
 Nov 4    
 Nov 6    
 Nov 11    
 Nov 13    
 Nov 18    
 Nov 20    
 Nov 25  Thanksgiving holidays, no class.  
 Nov 27  Thanksgiving holidays, no class.  
 Dec 2    
 Dec 4    


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