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

Valli, Alberto

Ann. Mat. Pura Appl., IV. Ser. 132, 399-400 (1982).

[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.

MSC:

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

Keywords:

convergence; successive approximations

Citations:

Zbl 0599.76081

References:

[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