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Proceedings of the American Mathematical Society
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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 | References | Similar Articles | Additional Information

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
Email: gqchen@math.nwu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03946-4
PII: S 0002-9939(97)03946-4
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