| Abstract: | The three‐dimensional motion of an incompressible inviscid fluid is classically described by the Euler equations but can also be seen, following Arnold 1], as a geodesic on a group of volume‐preserving maps. Local existence and uniqueness of minimal geodesics have been established by Ebin and Marsden 16]. In the large, for a large class of data, the existence of minimal geodesics may fail, as shown by Shnirelman 26]. For such data, we show that the limits of approximate solutions are solutions of a suitable extension of the Euler equations or, equivalently, are sharp measure‐valued solutions to the Euler equations in the sense of DiPerna and Majda 14]. © 1999 John Wiley & Sons, Inc. |
