Incipient singularities in the Navier-Stokes equations

Eric D. Siggia; Alain Pumir

doi:10.1103/PhysRevLett.55.1749

Incipient singularities in the Navier-Stokes equations

Eric D. Siggia and Alain Pumir

Phys. Rev. Lett. 55, 1749 – Published 21 October 1985

Abstract

Infinite pointwise stretching in a finite time for general initial conditions is found in a simulation of the Biot-Savart equation for a slender vortex tube in three dimensions. Viscosity is ineffective in limiting the divergence in the vorticity as long as it remains concentrated in tubes. Stability has not been shown.

Received 3 June 1985

DOI:https://doi.org/10.1103/PhysRevLett.55.1749

Authors & Affiliations

Eric D. Siggia and Alain Pumir

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853 and Institute for Theoretical Physics, University of California, Santa Barbara, California 93106