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.
Some results for the line vortex equation
BERSELLI, LUIGI CARLO;
2002-01-01
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.File in questo prodotto:
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