A correction to the paper: ”An existence theorem for compressible viscous fluids”. (English) Zbl 0599.76082

[Concerns the author’s article reviewed above (Zbl 0599.76081)]. The proof of the convergence of the successive approximations is not complete. In fact, we have proved the existence of a subsequence \((\nu_{n_ k},\theta_{n_ k},\rho_{n_ k})\) which converges, but we cannot pass to the limit in (2.4), (2.5) and (2.6), without proving that \((\nu_{n_ k-1},\theta_{n_ k-1},\rho_{n_ k-1})\) also converges to the same limit. This result does not seem easy to be proved, hence we prefer to utilize a slightly different approach. Acutally, we complete the proof of the existence of a solution by a fixed point argument.


76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q99 Partial differential equations of mathematical physics and other areas of application


Zbl 0599.76081
Full Text: DOI


[1] P.Secchi - A.Valli,A free boundary problem for compressible viscous fluids, J. Reine Angew. Math., to appear. · Zbl 0596.76084
[2] A. Valli,An existence theorem for compressible viscous fluids, Ann. Mat. Pura Appl.,130 (1982), pp. 197–213. · Zbl 0599.76081
[3] A. Valli,Uniqueness theorems for compressible viscous fluids, expecially when the Stokes relation holds, Boll. Un. Mat. It., Anal. Funz. Appl.,18-C (1981), pp. 317–325. · Zbl 0484.76075
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