Fernández-Cara, Enrique; Guillén, Francisco; Ortega, Rubens R. 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 C. R. Acad. Sci., Paris, Sér. I 319, No. 4, 411-416 (1994). 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. Cited in 18 Documents MSC: 76A10 Viscoelastic fluids 35Q35 PDEs in connection with fluid mechanics Keywords:global solution PDFBibTeX XMLCite \textit{E. Fernández-Cara} et al., C. R. Acad. Sci., Paris, Sér. I 319, No. 4, 411--416 (1994; Zbl 0808.76005)