Multidimensional transonic shock waves and free boundary problems
We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and correspo...
| Egile Nagusiak: | , |
|---|---|
| Formatua: | Journal article |
| Hizkuntza: | English |
| Argitaratua: |
World Scientific Pub Co Pte Ltd
2022
|
| _version_ | 1826311586356133888 |
|---|---|
| author | Chen, G-QG Feldman, M |
| author_facet | Chen, G-QG Feldman, M |
| author_sort | Chen, G-QG |
| collection | OXFORD |
| description | We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and corresponding free boundary problems for the compressible Euler equations and related nonlinear partial differential equations (PDEs) of mixed type. The nonlinear PDEs under our analysis include the steady Euler equations for potential flow, the steady full Euler equations, the unsteady Euler equations for potential flow, and related nonlinear PDEs of mixed elliptic-hyperbolic type. The transonic shock problems include the problem of steady transonic flow past solid wedges, the von Neumann problem for shock reflection-diffraction, and the Prandtl-Meyer problem for unsteady supersonic flow onto solid wedges. We first show how these longstanding multidimensional transonic shock problems can be formulated as free boundary problems for the compressible Euler equations and related nonlinear PDEs of mixed type. Then we present an effective nonlinear method and related ideas and techniques to solve these free boundary problems. The method, ideas, and techniques should be useful to analyze other longstanding and newly emerging free boundary problems for nonlinear PDEs. |
| first_indexed | 2024-03-07T08:11:56Z |
| format | Journal article |
| id | oxford-uuid:fa0566a9-6f2e-4b13-a8ac-056d7dd1e90d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:11:56Z |
| publishDate | 2022 |
| publisher | World Scientific Pub Co Pte Ltd |
| record_format | dspace |
| spelling | oxford-uuid:fa0566a9-6f2e-4b13-a8ac-056d7dd1e90d2023-11-30T15:29:34ZMultidimensional transonic shock waves and free boundary problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fa0566a9-6f2e-4b13-a8ac-056d7dd1e90dEnglishSymplectic ElementsWorld Scientific Pub Co Pte Ltd2022Chen, G-QGFeldman, MWe are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and corresponding free boundary problems for the compressible Euler equations and related nonlinear partial differential equations (PDEs) of mixed type. The nonlinear PDEs under our analysis include the steady Euler equations for potential flow, the steady full Euler equations, the unsteady Euler equations for potential flow, and related nonlinear PDEs of mixed elliptic-hyperbolic type. The transonic shock problems include the problem of steady transonic flow past solid wedges, the von Neumann problem for shock reflection-diffraction, and the Prandtl-Meyer problem for unsteady supersonic flow onto solid wedges. We first show how these longstanding multidimensional transonic shock problems can be formulated as free boundary problems for the compressible Euler equations and related nonlinear PDEs of mixed type. Then we present an effective nonlinear method and related ideas and techniques to solve these free boundary problems. The method, ideas, and techniques should be useful to analyze other longstanding and newly emerging free boundary problems for nonlinear PDEs. |
| spellingShingle | Chen, G-QG Feldman, M Multidimensional transonic shock waves and free boundary problems |
| title | Multidimensional transonic shock waves and free boundary problems |
| title_full | Multidimensional transonic shock waves and free boundary problems |
| title_fullStr | Multidimensional transonic shock waves and free boundary problems |
| title_full_unstemmed | Multidimensional transonic shock waves and free boundary problems |
| title_short | Multidimensional transonic shock waves and free boundary problems |
| title_sort | multidimensional transonic shock waves and free boundary problems |
| work_keys_str_mv | AT chengqg multidimensionaltransonicshockwavesandfreeboundaryproblems AT feldmanm multidimensionaltransonicshockwavesandfreeboundaryproblems |