Apriori estimates on the semiaxis $t\geqslant0$ for solutions of equations of motion of linear viscoelastic fluids with infinite Dirichlet integral and their applications

Global solvability on the semiaxis $t\geqslant0$ initial value problems for equations of motion of linear viscoelastic fluids with following external forse $f(x,t):f,f_t\in L_\infty(\mathrm{R}^+;L_2(\Omega))$ is investigated. Existence time periodicity of “small” smooth stable solutions of equations of motion of Oldroyd type fluids and Kelvin–Voight type fluids with “small” time periodicity external forse $f$ is proved.