Abstract. We consider an ideal fluid with vorticity concentrated on a smooth curve and we study an approximate model for the evolution of a line vortex. We prove existence and uniqueness of solutions in suitable Sobolev spaces, together with some blow-up estimates, near the possible singularities. We also prove a continuation criterion involving the length of the line itself.

Mathematics Subject Classification: 76B47, 76B03, 45K05

Print publication: Issue 6 (November 2002)
Received 22 January 2002
Published 9 September 2002