Volume 25, 2019
|Number of page(s)||37|
|Published online||25 September 2019|
A solution with free boundary for non-Newtonian fluids with Drucker–Prager plasticity criterion
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* Corresponding author: email@example.com
Accepted: 17 June 2018
We study a free boundary problem which is motivated by a particular case of the flow of a non-Newtonian fluid, with a pressure depending yield stress given by a Drucker–Prager plasticity criterion. We focus on the steady case and reformulate the equation as a variational problem. The resulting energy has a term with linear growth while we study the problem in an unbounded domain. We derive an Euler–Lagrange equation and prove a comparison principle. We are then able to construct a subsolution and a supersolution which quantify the natural and expected properties of the solution; in particular, we show that the solution has in fact compact support, the boundary of which is the free boundary.
The model describes the flow of a non-Newtonian material on an inclined plane with walls, driven by gravity. We show that there is a critical angle for a non-zero solution to exist. Finally, using the sub/supersolutions we give estimates of the free boundary.
Mathematics Subject Classification: 76A05 / 49J40 / 35R35
Key words: Non-Newtonian fluid / Drucker–Prager plasticity / variational inequality / free boundary
© EDP Sciences, SMAI 2019
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