Luigi C Berselli and Hakima Bessaih 2002 Nonlinearity 15 1729 doi:10.1088/0951-7715/15/6/301
Luigi C Berselli and Hakima Bessaih
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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.
45K05 Integro-partial differential equations (See also 34K30, 35R10, 47G20)
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
35A07 Local existence and uniqueness theorems (See also 35Hxx, 35Sxx)
76B03 Existence, uniqueness, and regularity theory (See also 35Q35)
Issue 6 (November 2002)
Received 22 January 2002
Published 9 September 2002
Luigi C Berselli and Hakima Bessaih 2002 Nonlinearity 15 1729
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