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Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state

Rickard, C; Hadžić, M; Jang, J; (2021) Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state. Nonlinearity , 34 (1) pp. 33-91. 10.1088/1361-6544/abb03b. Green open access

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Abstract

Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants γ > 1 is shown through perturbations around a rich class of background nonisentropic affine motions. The notable feature of the nonisentropic motion lies in the presence of non-constant entropies, and it brings a new mathematical challenge to the stability analysis of nonisentropic affine motions. In particular, the estimation of the curl terms requires a careful use of algebraic, nonlinear structure of the pressure. With suitable regularity of the underlying affine entropy, we are able to adapt the weighted energy method developed for the isentropic Euler Hadžić and Jang (2018 Inventiones Mathematicae214 1205–1266) to the nonisentropic problem. For large γ values, inspired by Shkoller and Sideris (2019 Arch. Ration. Mech. Anal.234 115), we use time-dependent weights that allow some of the top-order norms to potentially grow as the time variable tends to infinity. We also exploit coercivity estimates here via the fundamental theorem of calculus in time variable for norms which are not top-order.

Type: Article
Title: Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6544/abb03b
Publisher version: https://doi.org/10.1088/1361-6544/abb03b
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10117184
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