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- Anne C Morlet
- 1997

To develop an understanding of singularity formation in vortex sheets, we consider model equations that exhibit shared characteristics with the vortex sheet equation but are slightly easier to analyze. A model equation is obtained by replacing the ux term in Burgers' equation by alternatives that contain contributions depending globally on the solution. We… (More)

The overlapping sinc{collocation domain decomposition method combined with the Schwarz alternating technique is developed for two-point boundary-value problems for second-order ordinary diierential equations with singularities. The discrete system is formulated and the solution technique is described. It is shown that this method has an exponential… (More)

The sinc{collocation overlapping method is developed for two-point boundary-value problems for second-order ordinary diierential equations. The discrete system is formulated and the bordering algorithm used for the solution of this system is described. It is then shown that the convergence rate is exponential even if the solution has boundary singularities.… (More)

- Anne C Morlet
- 1997

Here, we rigorously prove some of the results obtained with asymp-totic methods for a modiied Burgers' equation, obtained by replacing the ux term in Burgers' equation considered in its hyperbolic form by the Hilbert transform. We show that, under the asumptions ju x j 1 C ?1=3 , jH(u x)j 1 C ?1=3 , and R 1 0 jju x jj 2 dt C, H(u) being the Hilbert… (More)

- Anne C Morlet
- 1997

We present an improved model for the vortex sheet equation, that combines some of the features of the models of Beale and Schaeeer, Dhanak, and Baker et al. We regularize the Beale-Schaeeer equation with a second-order viscous regularizing term, and we add a globally deened ux term in conservative form. We obtain u t + iu x = H(u)u ]x + ju x j 2 u x ]x + u… (More)

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