On vacuum points and the possibility of a Liouville theorem for compressible potential flows. I

✍ Scribed by J.W. Reyn

• Book ID: 104426659
• Publisher: Elsevier Science
• Year: 1970
• Weight: 559 KB
• Volume: 73
• Category: Article
• ISSN: 1385-7258
• DOI: 10.1016/s1385-7258(70)80016-6

✦ Synopsis

Solutions of Chaplygin's eq uat ion with y =3 for the initial value problem with analytic initial data on the vacuum line are used a s a basis for a classification of vacuum points. Three typos of vacuum points are distinguished: (i) points of the gen eration type, (ii) p oints of the r eflection type, (iii ) vacuum limit points. A vacuum limit point may either lie on a supersonic limit line or be isolated .

It is conjectured that a Li ou ville theorem for com p ressible po tential flows ex ist s, stating that the uniform flow is the on ly com pressible poten tial flow fr ee of limit lines and vacuum reflection lines throughout the entire flow plane.