Axially symmetric jet flows

A general existence and uniqueness theorem for three-dimensional axially symmetric jet flow is established. The existence of an absolute minimizer of a sequence of functionals is established and the coincidence set psi sub lambda equals Q is studied as a function of lambda. A general lemma on the convergence of free boundaries of psi sub lambda sub n to the free boundary of psi sub lambda, when lambda sub n goes to lambda, is proved. A lemma for a horizontal coincidence interval is also proved, and it is demonstrated that the free boundary is a curve x equals k(y). The definition of the solution of the jet problem is given, and monotonicity in lambda is shown. A bounded gradient lemma is proved, and a smooth fit at the point of detachment is shown. A continuous fit for psi is established, and the existence and uniqueness theorems are summarized. Finally, the shape of the free boundary is discussed.