Séminaire d'analyse
Compressible Euler equations: uniqueness and vacuumAnimesh Jana (TIFR-CAM, Bangalore, India)
Thursday 24 March 2022 14:00 - Tours - E2290
Résumé :
The motion of a compressible non-viscous fluid is governed by the Euler equations. In multi-D dimension,
the well-posedness of entropy solution is an open question. The existence of infinitely many entropy
solutions for Riemann type planar data has been shown in [1]. We have proved [2, 4] the uniqueness
of Holder continuous solution in the set of weak solutions satisfying entropy conditions. To prove the
uniqueness we have imposed (i) 1/2 H ̈older regularity and (ii) a one-sided Lipschitz bound condition. In
[3] we have shown the weak-strong uniqueness for the isentropic Euler system when the strong solution
may contain a vacuum region. In order to achieve the uniqueness result with vacuum, we imposed an
integrability condition on reciprocal of the density function.
References
[1] E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas
dynamics, Comm. Pure Appl. Math., 68, 1157–1190, 2015.
[2] E. Feireisl, S. S. Ghoshal and A. Jana, On uniqueness of dissipative solutions to the isentropic Euler
system, Comm. Partial Differential Equations, 44, no. 12, 1285–1298, (2019).
[3] S. S. Ghoshal, A. Jana and E. Wiedemann, Weak-Strong Uniqueness for the Isentropic Euler
Equations with Possible Vacuum. Preprint (submitted to journal) arxiv:2103.16560
[4] S. S. Ghoshal and A. Jana, Uniqueness of dissipative solutions to the complete Euler system. J.
Math. Fluid Mech. 23, no. 2, Paper No. 34, 25 pp, 2021.
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