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We are concerned with isentropic gas flow in the Laval nozzle with a frictiondue to viscosity. It is well known that the flow attains the sonic state at thethroat, where the cross section is minimum in the Laval nozzle. However, thepresent friction changes the position of the sonic state into downstream, whichis called chooking. Our goal in this paper is to investigate this phenomenamathematically. From the mathematical point of view, the friction is differentfrom normal frictions and difficult to treat with. In spite of its physicalimportance, the friction has not received much attention until now. For thecase without friction, the global existence of a solution was obtained byauthor. However, for the case with the friction, there are only restrictiveresults. The most difficult point is to obtain the bounded estimate ofsolutions. To solve this problem, we introduce an invariant region depending onthe mass. Adjusting the invariant region, we invent a new difference scheme,which yields approximate solutions including the mass.

Global existence of a solution for isentropic gas flow in the Laval nozzle with a friction