Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations
The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong transonic shocks under the perturbation of the upstream supersonic...
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| Format: | Journal article |
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European Mathematical Society
2018
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| _version_ | 1826258151146520576 |
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| author | Chen, G Chen, J Feldman, M |
| author_facet | Chen, G Chen, J Feldman, M |
| author_sort | Chen, G |
| collection | OXFORD |
| description | The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong transonic shocks under the perturbation of the upstream supersonic flow and the wedge boundary is proved. The problem is formulated as a one-phase free boundary problem, in which the transonic shock is treated as a free boundary. The full Euler equations are decomposed into two algebraic equations and a first-order elliptic system of two equations in Lagrangian coordinates. With careful elliptic estimates by using appropriate weighted Hölder norms, the iteration map is defined and analyzed, and the existence of its fixed point is established by performing the Schauder fixed point argument. The careful analysis of the asymptotic behavior of the solutions reveals particular characters of the full Euler equations. |
| first_indexed | 2024-03-06T18:29:29Z |
| format | Journal article |
| id | oxford-uuid:0926e8ca-11fe-4b75-a8f6-8f97b86b0f85 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:29:29Z |
| publishDate | 2018 |
| publisher | European Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:0926e8ca-11fe-4b75-a8f6-8f97b86b0f852022-03-26T09:16:40ZStability and asymptotic behavior of transonic flows past wedges for the full Euler equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0926e8ca-11fe-4b75-a8f6-8f97b86b0f85Symplectic Elements at OxfordEuropean Mathematical Society2018Chen, GChen, JFeldman, MThe existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong transonic shocks under the perturbation of the upstream supersonic flow and the wedge boundary is proved. The problem is formulated as a one-phase free boundary problem, in which the transonic shock is treated as a free boundary. The full Euler equations are decomposed into two algebraic equations and a first-order elliptic system of two equations in Lagrangian coordinates. With careful elliptic estimates by using appropriate weighted Hölder norms, the iteration map is defined and analyzed, and the existence of its fixed point is established by performing the Schauder fixed point argument. The careful analysis of the asymptotic behavior of the solutions reveals particular characters of the full Euler equations. |
| spellingShingle | Chen, G Chen, J Feldman, M Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations |
| title | Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations |
| title_full | Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations |
| title_fullStr | Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations |
| title_full_unstemmed | Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations |
| title_short | Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations |
| title_sort | stability and asymptotic behavior of transonic flows past wedges for the full euler equations |
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