Abstract
In this book we deal with two examples of systems of conservation laws, namely the barotropic compressible Euler equations (1.1), (1.2) and the full compressible Euler equations (1.6)–(1.8), both of which are introduced in Chap. 1. In this chapter we show that those two systems are indeed hyperbolic conservation laws as treated in Chap. 2.
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Notes
- 1.
- 2.
More precisely m denotes the momentum density and E the energy density.
- 3.
Here it is crucial that we are considering the multi-dimensional case, i.e. n ≥ 2.
- 4.
Here again it is essential that n ≥ 2.
- 5.
Keeping in mind that \(\mathbb {A}\) and \(\mathbb {B}\) are symmetric, we write ∗ for the entries in the upper triangle for convenience.
- 6.
Again note that in the context of the full Euler system, we use a modified notion of admissibility, see the remark above.
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Markfelder, S. (2021). The Euler Equations as a Hyperbolic System of Conservation Laws. In: Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations. Lecture Notes in Mathematics, vol 2294. Springer, Cham. https://doi.org/10.1007/978-3-030-83785-3_3
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DOI: https://doi.org/10.1007/978-3-030-83785-3_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-83785-3
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