Blow-up of Oskolkov's system of equations

Oskolkov's system of equations with a cubic source is considered; this describes the dynamics of a viscoelastic fluid. Local solvability (with respect to time) of the problem in the weak generalized sense is proved. Some conditions on the initial function which ensure that the solution blows up in finite time are found, and two-sided estimates for the existence time of the solution are obtained. Moreover, sufficient conditions for the global solvability (with respect to time) of the problem are found.
Bibliography: 19 titles.