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The existence and uniqueness of a local strong solution for non-Newtonian fluids of Oldroyd type (the \(L^ s-L^ r\) version). (Existence et unicité de solution forte locale en temps pour des fluides non newtoniens de type Oldroyd (version \(L^ s-L^ r)\).) (French. Abridged English version) Zbl 0808.76005

Summary: We present several existence and uniqueness results for the equations satisfied by the three-dimensional non-Newtonian fluids of the Oldroyd type. We prove that a strong local solution exists (and also that a global solution exists if the data are small). The results are established in a \(L^ s- L^ r\) framework; in particular, the uniqueness result is the analogue of the well known local in time uniqueness result for the Navier-Stokes problem.

MSC:

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

Keywords:

global solution
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