An example of self–acceleration for incompressible flows

Jens Lorenz; Randy Ott

doi:10.5269/bspm.v31i2.17308

An example of self–acceleration for incompressible flows

Authors

Jens Lorenz Department of Mathematics and Statistics, UNM, Albuquerque, NM 87131
Randy Ott Department of Mathematics and Statistics, UNM, Albuquerque, NM 87131

DOI:

https://doi.org/10.5269/bspm.v31i2.17308

Keywords:

incompressible flows, Euler equation, Navier-Stokes equation, self-acceleration

Abstract

In this paper we consider the Cauchy problem for the unforced Eulerand Navier–Stokes equations for incompressible flows. We give an example of a smooth initial velocity field of finite energy which is self-accelerating, i.e., the maximal speed increases for some time. The self–acceleration is due to the non–Bernoulli part of the pressure generated by the velocity field.