### An Example of Self–Acceleration for Incompressible Flows

#### 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.

#### Keywords

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

#### Full Text:

PDFDOI: http://dx.doi.org/10.5269/bspm.v31i2.17308

ISSN 0037-8712 (print) and ISSN 2175-1188 (on-line)