Remarks on DiPerna's paper - ''Convergence of the viscosity method for isentropic gas dynamics''

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. Out 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.