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Remarks on DiPerna's Paper ``Convergence of the Viscosity Method for Isentropic Gas Dynamics' |
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| Authors: | Gui-Qiang Chen |
| Affiliation: | Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730 |
| 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. |
| Keywords: | DiPerna's lemma remarks gap fix bypass viscosity method finite difference methods isentropic Euler equations |
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