A. M. Blokhin, A. V. Yegitov, D. L. Tkachev, “Linear instability of solutions in a mathematical model describing polymer flows in an infinite channel”, Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 5,Pages <nobr>850

This article is cited in 29 papers

Linear instability of solutions in a mathematical model describing polymer flows in an infinite channel

A. M. Blokhin^ab, A. V. Yegitov^ba, D. L. Tkachev^ba

^a Novosibirsk State University, Pirogova st. 2, Novosibirsk, 630090, Russia
^b Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Koptyug av. 4, Novosibirsk, 630090, Russia

Abstract: A new rheological model describing flows of incompressible viscoelastic polymer fluid is studied. Lyapunov’s linear instability of the Poiseuille flow counterpart for the Navier–Stokes equations in a plane infinite channel is proven.

Key words: incompressible viscoelastic polymer fluid, rheological relationship, Brownian particle, dumbbell, Poiseuille solution, well-posedness of mixed problem, linear instability of solutions.

UDC: 519.634

MSC: Primary 76A10; Secondary 35Q35, 82D60

Received: 19.06.2013
Revised: 26.06.2014

DOI: 10.7868/S0044466915050075