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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf6359https://doi.org/10.4213/tmf6359 https://www.mathnet.ru/eng/tmf/v159/i3/p399
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