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Existence of classical solutions for compressible viscoelastic fluids of Oldroyd type past an obstacle. (English) Zbl 0916.76004
Summary: We show the existence and uniqueness of stationary solutions for the equations modelling the steady flow of compressible viscoelastic fluids of Oldroyd type in an exterior domain. The proof is based on an appropriate decomposition of the original nonlinear equations into auxiliar problems (Neumann problems for the Laplacian, Oseen problem, two transport equations), and on a fixed point argument in a suitable functional setting.

MSC:
76A10 Viscoelastic fluids
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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