Abstract.
A compressible one-dimensional plain Bingham flow starting in equilibrium under the action of a time-increasing spatially homogeneous mass force is investigated. A lower estimate for the width of a rigid zone is obtained. The estimate shows that the rigid zone converges to the whole interval for t tends to zero. In other words, existence of a rigid core is established.
As a supplementary result, additional smoothness of solutions to the system considered is established.
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Basov, I.V. Existence of a Rigid Core in the Flow of a Compressible Bingham Fluid under the Action of a Homogeneous Force. J. math. fluid mech. 7, 515–528 (2005). https://doi.org/10.1007/s00021-005-0179-1
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DOI: https://doi.org/10.1007/s00021-005-0179-1