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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 3, Pages 399–410
DOI: https://doi.org/10.4213/tmf6359 (Mi tmf6359) 		 
Riemann-invariant solutions of the isentropic fluid flow equations

R. Contea, A. M. Grundlandb, B. Huardc

a École normale supérieure de Cachan
b Université du Québec à Trois-Rivières
c Université de Montréal, Centre de Recherches Mathématiques
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DOI: https://doi.org/10.4213/tmf6359
Abstract: We use a new version of the conditional symmetry method to obtain rank-$k$ solutions expressed in terms of Riemann invariants of the isentropic compressible ideal fluid flow in $3+1$ dimensions. We describe the procedure for constructing bounded solutions in terms of the elliptic Weierstrass $\wp$-function in detail.
Keywords: Riemann invariant, conditional symmetry method, rank-$k$ solution, system of hydrodynamic type.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 3, Pages 752–762
DOI: https://doi.org/10.1007/s11232-009-0063-x
Bibliographic databases:
Language: Russian
Citation: R. Conte, A. M. Grundland, B. Huard, “Riemann-invariant solutions of the isentropic fluid flow equations”, TMF, 159:3 (2009), 399–410; Theoret. and Math. Phys., 159:3 (2009), 752–762
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v159/i3/p399
    • Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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