Non-homogeneous Perfect Fluid

The Euler equations for a non-homogeneous, non-viscous ~ompressible fluid are shown to be well-posed for a short time interval~ using techniques of infinite dimensional geometry and a weighted Hodge theorem. Regularity and other properties of these solutions are pointed out as well. !. Introduction. In [2], D. Ebin and the author introduced a technique for solving the Euler equations for a perfect (homogeneous, non-viscous, incompressible) fluid based on the use of the group JD~ of Sobolev class HS(or Ws,p or Holder class ck+a ) volume preserving diffeomorphisms. This method originated in an idea of V. Arnold [1]. 215 Copyright cO 1976 by Marcel Dekker. Inc. All Rights Reserved. Neither this work nor any part may be reproduced or transmitted in any form or by any means. electronic or mechanical. indudina photocopyinS. microrilmins. wnd recordins. or by any information storage and retrieval system. without permission in writina from the publisher.