This leading order equation captures the most singular contribution of the integral equation. This rather surprising result confirms that the tangential velocity jump is the physical driving force of the vortex sheet singularities. The existence time can be arbitrarily close to the singularity time predicted by the leading order equation when the initial condition is near equilibrium. A generalized Moore's approximation to 3-D vortex sheets is introduced. Detailed numerical study will be provided to support the analytic results, and to reveal the generic form of the three-dimensional nature of the vortex sheet singularity.
Spectral projections enjoy superior resolution provided the data is globally smooth.
Gibbs oscillations in the neighborhood of such jumps, and an overall deterioration to the unacceptable first-order convergence rate of spectral projections. A detection procedure which based on appropriate choice of concentration factors which identify finitely many edges - both their location and their amplitudes. We present a two-parameter family of spectral mollifiers which recover the data between the edges with exponential accuracy. November 29, S.R.S. Varadhan, New York University Scaling limits of Interacting Particle Systems We will review the types of result known on the asymptotic behavior under scaling of interacting particle systems. We will use as examples the various types of simple exclusion processes.