Starting from the Navier-Stokes equation, we rigorously prove that a modi ed third order structure function ~ S 3 (r) asymptotically equals 4 r=3 ( is the dissipation rate) in the large Reynoldsâ€¦ (More)

Streamer discharges determine the very first stage of sparks or lightning, and they govern the evolution of huge sprite discharges above thunderclouds as well as the operation of corona reactors inâ€¦ (More)

The particular example given in Â§6 of Crowdy and Tanveer [1] to illustrate the general theory is in error because it is not consistent with the original assumptions underlying the theory. The theoryâ€¦ (More)

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a â€˜kinetic undercoolingâ€™ boundary condition.â€¦ (More)

This paper is concerned with proving global existence and stability of a translating bubble in a Hele-Shaw cell that is small relative to cell width. When the ratio of cell width to bubble dimensionâ€¦ (More)

Two cases of evolution of interfaces in axi-symmetric Stokes flow are considered: 1) a bubble whose volume changes with time and 2) a viscous drop whose interior and exterior fluids have differentâ€¦ (More)

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a â€˜kinetic undercoolingâ€™ boundary condition. Weâ€¦ (More)

We present a new numerical method for calculating an evolving 2-D Hele-Shaw interface when surface tension e ects are neglected. In the case where the ow is directed from the less viscous uid intoâ€¦ (More)

In this paper, we consider analytic initial conditions with nite energy, whose complex spatial continuation is a superposition of a smooth background ow and a singular eld. Through explicitâ€¦ (More)