Full paper in PDF:
$%L. Santos, On the variational inequality approach to compressible flows via hodograph method, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 2, 333374.%$

On the Variational Inequality Approach to Compressible Flows Via Hodograph Method
Departamento de Matemática
Universidade do Minho
Campus de Gualtar
4700 Braga Portugal

Received: December 30, 1992

We study the flow of a compressible, stationary and irrotational fluid with wake, in a channel, around a convex symmetric profile, with assigned velocity q oo  at infinity and qs < q oo  at the wake. In particular, we study the regularity of the free boundary (for a problem which has non-constant coefficients), in the hodograph plane.

Using variational inequalities, we obtain the solutions of some known cases as limit of this one, namely the solutions of the problems of an incompressible fluid in a channel without wake, in the plane with and without wake, and the problem if a compressible fluid in the plane.

We also study the convergence of the free boundary of the new problem to the free boundaries of the limit corresponding problems.

1991 Mathematics Subject Classification: 35J85.