An existence theorem in compressible fluid dynamics
Abstract
Consideration is given to the equations of motion of a nonviscous, compressible, barotropic fluid in a bounded domain of three or two dimensional Euclidian space. It is shown that there exists a nondecreasing function of the norms of the initial velocity and density, the volume force density and its first and second derivatives which is dependent only on those norms, the domain and the pressure, and for which there is a unique solution of the equations for fluid velocity and density in Sobolev space of order 3, 2 or 1. It is noted that corresponding solutions may also be obtained for Sobolev spaces of higher order.
 Publication:

Academie des Sciences Paris Comptes Rendus Serie B Sciences Physiques
 Pub Date:
 December 1979
 Bibcode:
 1979CRASB.289..297B
 Keywords:

 Barotropic Flow;
 Compressible Fluids;
 Existence Theorems;
 Flow Theory;
 Inviscid Flow;
 Fluid Dynamics;
 Fluid Mechanics and Heat Transfer