Electron. J. Differential Equations, Vol. 2018 (2018), No. 94, pp. 1-11.

Contact discontinuities in multi-dimensional isentropic Euler equations

Jan Brezina, Elisabetta Chiodaroli, Ondrej Kreml

In this note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove non-uniqueness of admissible weak solutions that start from the Riemann initial data allowing a contact discontinuity to emerge.

Submitted July 10, 2017. Published April 19, 2018.
Math Subject Classifications: 35L65, 35L45, 35Q35, 76N10.
Key Words: Isentropic Euler equations; non-uniqueness; Riemann problem; admissible weak solutions; contact discontinuity.

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Jan Brezina
Tokyo Institute of Technology
2-12-1 Ookayama, Meguro-ku
Tokyo, 152-8550, Japan
email: brezina@math.titech.ac.jp
Elisabetta Chiodaroli
Dipartimento di Matematica
Universita di Pisa
Via F. Buonarroti 1/c, 56127 Pisa, Italy
email: elisabetta.chiodaroli@unipi.it
Ondrej Kreml
Institute of Mathematics
Czech Academy of Sciences
Zitna 25, Prague 1, 115 67, Czech Republic
email: kreml@math.cas.cz

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