On solvability of a nonstationary problem of the dynamics of the incompressible viscoelastic nonzeroth order Kelvin-Voigt fluid
The author proves existence theorem for an abstract Cauchy problem for semilinear non-stationary equation of the Sobolev type, and then treats a Cauchy-Dirichlet problem for the incompressible viscoelastic Kelvin-Voigt fluid as a particular case of the abstract problem. The results of the paper generalize the results by \textit{G. A. Sviridyuk} [Russ. Math. 38, No. 1, 59-68 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 1(380), 62-70 (1994; Zbl 0828.76010)].
semilinear nonstationary equation of Sobolev type
incompressible viscoelastic Kelvin-Voigt fluid
scientific article; zbMATH DE number 1309927