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Limites des √©quations d’un fluide compressible lorsque la compressibilit√© tend vers zero. (English) Zbl 0544.76072
Fluid dynamics, Lect. 3rd Sess. C.I.M.E., Varenna/Italy 1982, Lect. Notes Math. 1047, 139-165 (1984).
[For the entire collection see Zbl 0523.00017.]
The author considers the existence of solutions of the well known gasdynamic equations for the case that the compressibility tends to zero. To show local existence in time his work depends upon papers of J. Nash [Bull. Soc. Math. Fr. 90, 487-497 (1962; Zbl 0113.19405)], N. Itaya [(*) Kodai Math. Sem. Rep. 23, 60-120 (1971; Zbl 0219.76080)], and for global existence in time his work corresponds to papers of Ya. I. Kanel [Differ. Uravn. 4, 721-734 (1968; Zbl 0164.40803)], N. Itaya (*), A. V. Kazhikow and V. V. Seluhin [J. Appl. Math. Mech. 41, 273-282 (1977; Zbl 0393.76043)]. The authors methods to handle the mathematical problem are very similar e.g. to those by T. Nishida and A. Matsumura [J. Math. Kyoto Univ. 20, 67-104 (1980; Zbl 0429.76040)].
Reviewer: W.F.Schmidt
MSC:
76N15 Gas dynamics (general theory)