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Three-dimensional steady flow of viscoelastic fluid past an obstacle. (English) Zbl 0974.35094
Summary: The authors examine three-dimensional steady flows of a general class of viscoelastic fluids (which includes, as particular cases, corotational, lower convective and upper convective Maxwell fluids) in exterior domains with arbitrary non-zero velocity at infinity. The main result states that the solution behaves at infinity as the fundamental solution of the Oseen problem. The proof employs a decomposition of the original problem into a linear problem governed by transport equations, and a modified Oseen problem which, nevertheless, has the same asymptotic solution at infinity as the classical Oseen problem. Then the authors use weighted estimates and an iterative procedure based on Banach fixed point theorem.

35Q35 PDEs in connection with fluid mechanics
76A10 Viscoelastic fluids
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