Well-posedness for a class of non-Newtonian fluids with general growth conditions

Abstract

The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-lawtype rheology. We describe the growth conditions with the help of general x-dependent convex functions. This formulation yields the existence of solutions in generalized Orlicz spaces. These considerations are motivated by e.g. electrorheological fluids, magnetorheological fluids, and shear thickening fluids.

On the dynamic instability of non‐Newtonian fluids driven by gravity

“…Even so, there are many important progress on theoretical analysis for non-Newtonian fluid systems, Bothe-Pruss have given the result of the L p -theory for a class of non-Newtonian fluids [4]; Feireisl-Kwon investigated the long-time behavior of dissipative solutions to models of non-Newtonian compressible fluids [5]; Guo-Tan have given the result of large-time behavior of solutions to a class of non-Newtonian compressible fluids [6]. The results of the well-posedness for non-Newtonian fluids can be refer to [7][8][9][10][11] for details. For more results of non-Newtonian fluids, please refer to [2,6,[10][11][12][13][14][15][16] and the references cited therein.…”