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- W2006474102 abstract "We present an α-regularization of the Birkhoff-Rott equation (BR-α equation), induced by the two-dimensional Euler-α equations, for the vortex sheet dynamics. We show the convergence of the solutions of Euler-α equations to a weak solution of the Euler equations for initial vorticity being a finite Radon measure of fixed sign, which includes the vortex sheets case. We also show that, provided the initial density of vorticity is an integrable function over the curve with respect to the arc length measure, (i) an initially Lipschitz chord arc vortex sheet (curve), evolving under the BR-α equation, remains Lipschitz for all times, (ii) an initially Hölder C1, β, 0 ≤ β < 1, chord arc curve remains in C1, β for all times, and finally, (iii) an initially Hölder Cn, β, n ≥ 1, 0 < β < 1, closed chord arc curve remains so for all times. In all these cases the weak Euler-α and the BR-α descriptions of the vortex sheet motion are equivalent. © 2009 Wiley Periodicals, Inc." @default.
- W2006474102 created "2016-06-24" @default.
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- W2006474102 date "2010-06-01" @default.
- W2006474102 modified "2023-09-26" @default.
- W2006474102 title "Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the two-dimensional Euler equations" @default.
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- W2006474102 doi "https://doi.org/10.1002/cpa.20305" @default.
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