Shock waves with irrotational Rankine-Hugoniot conditions
Authors:
Dening Li and Qingtian Zhang
Journal:
Quart. Appl. Math.
MSC (2020):
Primary 35F55, 35L67, 76L05, 76N30; Secondary 35L15
DOI:
https://doi.org/10.1090/qam/1682
Published electronically:
October 23, 2023
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Additional Information
Abstract: Shock wave stability for isentropic irrotational flow is studied for Euler system but with shock front conditions corresponding to the second order nonlinear wave equation. It is shown that the usual Lax’ shock condition still guarantees the uniform linear stability and therefore the existence of the shock waves solution.
References
- An Ton Bui and De Ning Li, Double shock fronts for hyperbolic systems of conservation laws in multidimensional space, Trans. Amer. Math. Soc. 316 (1989), no. 1, 233–250. MR 935939, DOI 10.1090/S0002-9947-1989-0935939-1
- Shuxing Chen and Dening Li, Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system, J. Differential Equations 257 (2014), no. 6, 1939–1988. MR 3227287, DOI 10.1016/j.jde.2014.05.027
- ShuXing Chen and DeNing Li, Generalised Riemann problem for Euler system, Sci. China Math. 60 (2017), no. 4, 581–592. MR 3629484, DOI 10.1007/s11425-016-0437-x
- R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948. MR 29615
- Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI 10.1002/cpa.3160230304
- De Ning Li, Rarefaction and shock waves for multidimensional hyperbolic conservation laws, Comm. Partial Differential Equations 16 (1991), no. 2-3, 425–450. MR 1104106, DOI 10.1080/03605309108820764
- D. Li and Q. Zhang, Double shock solution for 3-dimensional irrotational isentropic flow, J. Hyperbolic Diff. Eq. (to appear).
- Andrew Majda, The existence of multidimensional shock fronts, Mem. Amer. Math. Soc. 43 (1983), no. 281, v+93. MR 699241, DOI 10.1090/memo/0281
- Andrew Majda and Enrique Thomann, Multidimensional shock fronts for second order wave equations, Comm. Partial Differential Equations 12 (1987), no. 7, 777–828. MR 890631, DOI 10.1080/03605308708820509
- Maher Mnif, Problème de Riemann pour une loi de conservation scalaire hyperbolique d’ordre deux, Comm. Partial Differential Equations 22 (1997), no. 9-10, 1589–1627 (French). MR 1469583, DOI 10.1080/03605309708821312
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften, vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
References
- An Ton Bui and De Ning Li, Double shock fronts for hyperbolic systems of conservation laws in multidimensional space, Trans. Amer. Math. Soc. 316 (1989), no. 1, 233–250. MR 935939, DOI 10.2307/2001282
- Shuxing Chen and Dening Li, Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system, J. Differential Equations 257 (2014), no. 6, 1939–1988. MR 3227287, DOI 10.1016/j.jde.2014.05.027
- ShuXing Chen and DeNing Li, Generalised Riemann problem for Euler system, Sci. China Math. 60 (2017), no. 4, 581–592. MR 3629484, DOI 10.1007/s11425-016-0437-x
- R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, Interscience Publishers, Inc., New York, 1948. MR 29615
- Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI 10.1002/cpa.3160230304
- De Ning Li, Rarefaction and shock waves for multidimensional hyperbolic conservation laws, Comm. Partial Differential Equations 16 (1991), no. 2-3, 425–450. MR 1104106, DOI 10.1080/03605309108820764
- D. Li and Q. Zhang, Double shock solution for 3-dimensional irrotational isentropic flow, J. Hyperbolic Diff. Eq. (to appear).
- Andrew Majda, The existence of multidimensional shock fronts, Mem. Amer. Math. Soc. 43 (1983), no. 281, v+93. MR 699241, DOI 10.1090/memo/0281
- Andrew Majda and Enrique Thomann, Multidimensional shock fronts for second order wave equations, Comm. Partial Differential Equations 12 (1987), no. 7, 777–828. MR 890631, DOI 10.1080/03605308708820509
- Maher Mnif, Problème de Riemann pour une loi de conservation scalaire hyperbolique d’ordre deux, Comm. Partial Differential Equations 22 (1997), no. 9-10, 1589–1627 (French). MR 1469583, DOI 10.1080/03605309708821312
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften, vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
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Additional Information
Dening Li
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26505
MR Author ID:
194475
Email:
deli@mail.wvu.edu, dnli@hotmail.com
Qingtian Zhang
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26505
MR Author ID:
1015414
Email:
qingtian.zhang@mail.wvu.edu
Keywords:
Euler system,
isentropic and irrotational flow,
shock waves
Received by editor(s):
May 4, 2023
Received by editor(s) in revised form:
September 21, 2023
Published electronically:
October 23, 2023
Article copyright:
© Copyright 2023
Brown University
