Existence and stability results for 3-D regular flows of viscoelastic fluids of White--Metzner type
The authors generalize results obtained by \textit{A. Hakim} [J. Math. Anal. Appl. 185, No. 3, 675--705 (1994; Zbl 0807.76002)] for incompressible viscoelastic fluids of White-Metzner type. While Hakim studied the two-dimensional case, the main theorems here are concerned with (i) local existence and uniqueness of a regular solution in three dimensions; (ii) global existence of regular solutions in three dimensions; (iii) improved global existence in two dimensions (without the smallness restriction for the retardation parameter and the boundedness hypothesis on the relaxation function). Finally, by a classical stability argument, the existence and stability of small periodic and stationary solutions are obtained.
scientific article; zbMATH DE number 2105449
scientific article