Geodesic
On the diffusion of a rigid viscoplastic vortex layer
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 63-67.

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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, yield stress, vortex layer, nonsteady shear, disturbance, quadratic functional.
Mots-clés : rigid domain, diffusion 
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D. V. Georgievskii. On the diffusion of a rigid viscoplastic vortex layer. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 63-67. http://geodesic.mathdoc.fr/item/ND_2018_14_1_a5/

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[3] Georgiyevskii D. V., “Stability of the nonsteady shear of the Bingham medium in plane layer”, J. Appl. Math. Mech., 2018