Geodesic
Two-dimensional steady supersonic exothermically reacting Euler flows with strong contact discontinuity over a Lipschitz wall
Wei Xiang1 ; Yongqian Zhang2 ; Qin Zhao2
1City University of Hong Kong, Hong Kong
2Fudan University, Shanghai, China
Interfaces and free boundaries, Tome 20 (2018) no. 3, pp. 437-481

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DOI

In this paper, we establish the global existence of supersonic entropy solutions with a strong contact discontinuity over a Lipschitz wall governed by the two-dimensional steady exothermically reacting Euler equations, when the total variation of both the initial data and slope of the Lipschitz wall is sufficiently small. Local and global estimates are developed and a modified Glimm-type functional is carefully designed. Next the validation of the quasi-one-dimensional approximation in the domain bounded by the wall and the strong contact discontinuity is rigorous justified by proving that the difference between the average of weak solution and the solution of quasi-one-dimensional system can be bounded by the square of the total variation of both the initial data and slope of the Lipschitz wall.
DOI : 10.4171/ifb/408
Classification : 35-XX, 76-XX
Mots-clés : Supersonic flow, reacting Euler equations, Glimm scheme, fractional-step, Glimm functional, contact discontinuity, interface, stability, quasi-one-dimensional approximation

Wei Xiang  1   ; Yongqian Zhang  2   ; Qin Zhao  2

1 City University of Hong Kong, Hong Kong
2 Fudan University, Shanghai, China 
Wei Xiang; Yongqian Zhang; Qin Zhao. Two-dimensional steady supersonic exothermically reacting Euler flows with strong contact discontinuity over a Lipschitz wall. Interfaces and free boundaries, Tome 20 (2018) no. 3, pp. 437-481. doi: 10.4171/ifb/408
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     author = {Wei Xiang and Yongqian Zhang and Qin Zhao},
     title = {Two-dimensional steady supersonic exothermically reacting {Euler} flows with strong contact discontinuity over a {Lipschitz} wall},
     journal = {Interfaces and free boundaries},
     pages = {437--481},
     year = {2018},
     volume = {20},
     number = {3},
     doi = {10.4171/ifb/408},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/408/}
}
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