Remarks on DiPerna’s Paper “Convergence of the Viscosity Method for Isentropic Gas Dynamics”. (English) Zbl 0888.35066
Summary: Concerns have been voiced about the correctness of certain technical points in R. J. DiPerna’s paper [Commun. Math. Phys. 91, 1-30 (1983; Zbl 0533.76071)] 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.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35L60 | First-order nonlinear hyperbolic equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76N15 | Gas dynamics (general theory) |
Citations:
Zbl 0533.76071References:
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