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We prove a continuous dependence theorem for weak solutions of equations governing a fluid-structure interaction problem in two spatial dimensions. The proof is based on a priori estimates which, in particular, convey uniqueness of weak solutions. The estimates are obtained using Eulerian coordinates, without remapping the problem into a fixed domain.
We investigate plane steady ows of a viscous, isothermal, compressible uid past an obstacle, with nonzero velocity at innnity. Using the decomposition of the velocity eld onto its compressible and incompressible parts, we prove an existence and uniqueness theorem, under the assumption that the external data are \suuciently small".
We prove existence and a representation formula for solutions to the equations describing steady flows of an isothermal, viscous, compressible gas having a positive infi-mum for the density ̺, moving in an exterior domain, when the speed of the obstacle and the external forces are sufficiently small. 1. Introduction. In this paper we shall be concerned with… (More)