An Example of Self–Acceleration for Incompressible Flows

Randy Ott, Jens Lorenz


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.


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

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

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