Abstract
The initial‐boundary value problem for the mathematical model of low‐concentrated aqueous polymer solutions is considered. For this initial‐boundary value problem a concept of a weak solution is introduced and the existence theorem for such solutions is proved.
Highlights
The initial-boundary value problem for the mathematical model of low-concentrated aqueous polymer solutions is considered. For this initial-boundary value problem a concept of a weak solution is introduced and the existence theorem for such solutions is proved
The study of fluid motion is a source of a large number of mathematical problems
In the given system v(x,t) is the velocity vector of the particle at a point x at an instant t; p = p(x,t) is the pressure of the fluid at a point x at an instant t; f = f (x,t) is the vector of body forces acting on the fluid; σ = (σij(x)) is the deviator of the stress tensor
Summary
Motion of an incompressible fluid in a bounded domain Ω ⊂ Rn on a time interval [0, T], (T < ∞) is described by the following system of equations in Cauchy’s form [3]:. (x, t) ∈ Ω × [0, T], div v = 0, (x, t) ∈ Ω × [0, T]. By Div σ we denote the vector of divergences of columns of the matrix σ. The system of (1.1) describes formally the motion of all kinds of fluids. To complete the given system one usually uses various relations between the deviator of the stress tensor σ and the strain rate tensor Ᏹ = (Ᏹij), Ᏹi j.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
