In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.
more » « less- PAR ID:
- 10552044
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Living Reviews in Relativity
- Volume:
- 27
- Issue:
- 1
- ISSN:
- 1433-8351
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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