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# On the diffusion of a rigid viscoplastic vortex layer

2018, Vol. 14, no. 1, pp.  63-67

Author(s): Georgievsky D. V.

This paper is concerned with obtaining the parameters of a nonsteady shear rigid viscoplastic flow in a half-plane initially at rest. Beginning with the initial time moment, the constant tangent stress exceeding a yield stress is given on the boundary. The diffusion-vortex solution holds true inside an extending layer with an a priori unknown boundary. The remaining half-plane is immovable in this case. A two-dimensional picture of disturbances is imposed on the obtained flow; the picture may then evolve over time. The upper estimates of velocity disturbances by the integral measure of the space $H_2$ are constructed. It is shown that, in a certain range of parameters, the estimating function may decrease up to some point of minimum and only then increase exponentially. The fact of its initial decrease is interpreted as a stabilization of the main flow on a finite time interval.

Keywords: viscoplastic solid, rigid domain, yield stress, diffusion, vortex layer, nonsteady shear, disturbance, quadratic functional
Citation: Georgievsky D. V., On the diffusion of a rigid viscoplastic vortex layer, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  63-67
DOI:10.20537/nd1801006

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