On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium

Abstract: Unstationary and stationary two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the theological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson-Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solution was derived. Analysis of the analytical unstationary solution provides a new class of stationary solutions. The solutions found comprise both already known as well as substantially new solutions. Nonsingular solutions of the stress tensor at the critical point and bounded at infinity are constructed. Exact analytical formulae for the stress tensor with the Weissenberg number Wi=1/2 are obtained.

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machine learningmathematical softwaresymbolic computationmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemscomputational physicsdata analysis, statistics and probability

Audience: researchers in the topic

Mathematical models and integration methods