Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state
| Autor: | Calum Rickard, Juhi Jang, Mahir Hadžić |
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| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics 35Q31 76N10 76N15 35L70 35B35 01 natural sciences Euler equations 010101 applied mathematics symbols.namesake Mathematics - Analysis of PDEs Fundamental theorem of calculus FOS: Mathematics Compressibility symbols Euler's formula Affine transformation 0101 mathematics Algebraic number Adiabatic process Entropy (arrow of time) Mathematical Physics Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Nonlinearity. 34:33-91 |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/1361-6544/abb03b |
| Popis: | Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ 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 by Had\v{z}i\'c and Jang to the nonisentropic problem. For large $\gamma$ values, inspired by Shkoller and Sideris, 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. Comment: 52 pages, to appear in Nonlinearity. Please see arXiv:2007.03849 for a recent development in this direction |
| Databáze: | OpenAIRE |
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