THE STUDY OF ONE CLASS OF VISCOELASTIC FLUIDS WITH MEMORY
The article is devoted to the study of the weak solvability of the initial-boundary value problem for one class of viscoelastic fluids with memory. The type of the considered fluid is determined by a relation that is called the constitutive or rheological law. In this article, the constitutive law contains bounded measurable function what characterizes memory of particles of fluid. The main result of this work is the proof of the existence theorem of the weak solution of this initial-boundary value problem. For the proof of this theorem it is used approximating-topological method. This method was introduced by V. G. Zvyagin and was developed in his papers.