Well-posedness for a class of compressible non-Newtonian fluids equations

The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. The equations describing the motion of such fluids are characterized by a non-linear constitutive law relating the state of stress to the rate of deformation. We show the local-in-time existence and uniqueness of strong solutions to two important models: the Power Law model and the Bingham model. While our result for the first model holds over a periodic domain S2 = R3, the result obtained on the second model is limited to the one-dimensional case. This is because Bingham's constitutive law is discontinuous due to phase transition that may appear during the time when flows change nature, particularly from liquid motion to rigid motion and vice-versa. This property reduces the probability of showing smooth solutions to such a system in higher dimension space.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The purpose of this paper is to study the well-posedness of a class of non-Newtonian fluid dynamics equations. These equations have a non-linear constitutive relation that connects the stress state with the rate of deformation. We prove the local-in-time existence and uniqueness of strong solutions for two important models: the Power Law model and the Bingham model. The result for the Power Law model holds in a periodic domain, while the result for the Bingham model is limited to one-dimensional case due to its discontinuous constitutive relation caused by phase transitions during flow changes.