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Remarks on DiPerna’s paper “Convergence of the viscosity method for isentropic gas dynamics”

Author: Gui-Qiang Chen
Journal: Proc. Amer. Math. Soc. 125 (1997), 2981-2986
MSC (1991): Primary 35K55, 35L65; Secondary 76N15, 35L60, 65M06
MathSciNet review: 1403118
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Abstract: Concerns have been voiced about the correctness of certain technical points in DiPerna’s paper (Comm. Math. Phys. 91 (1983), 1–30) related to the vacuum state. In this note, we provide clarifications. Our conclusion is that these concerns mainly arise from the statement of a lemma for constructing the viscous approximate solutions and some typos; however, the gap can be either fixed by correcting the statement of the lemma and the typos or bypassed by employing the finite difference methods.

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Additional Information

Gui-Qiang Chen
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
MR Author ID: 249262
ORCID: 0000-0001-5146-3839

Keywords: DiPerna’s lemma, remarks, gap, fix, bypass, viscosity method, finite difference methods, isentropic Euler equations
Received by editor(s): May 16, 1996
Communicated by: James Glimm
Article copyright: © Copyright 1997 American Mathematical Society