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Remarks on DiPerna's Paper ``Convergence of the Viscosity Method for Isentropic Gas Dynamics''
Author(s):
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.
References:
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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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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