A General Convex Integration Scheme for the Isentropic Compressible Euler Equations
| Autor: | Dębiec, Tomasz, Skipper, Jack W. D., Wiedemann, Emil |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least $2$) to exact weak solutions. The method is closely related to the incompressible scheme established by De Lellis--Sz\'ekelyhidi, in particular we only perturb momenta and not densities. Surprisingly, though, this turns out not to be a restriction, as can be seen from our simple characterization of the $\Lambda$-convex hull of the constitutive set. An important application of our scheme will be exhibited in forthcoming work by Gallenm\"uller--Wiedemann. Comment: 21 pages |
| Databáze: | arXiv |
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