Some remarks about the stationary micropolar fluid equations: existence, regularity and uniqueness. (English) Zbl 1536.35256
Summary: We consider here the stationary micropolar fluid equations, which are a special generalization of the usual Navier-Stokes system where the microrotations of the fluid particles must be taken into account. We thus obtain two coupled equations: one mainly based on the velocity field \(\overrightarrow{u}\) and the other on the microrotation field \(\overrightarrow{\omega} \). In this work we will study some problems related to the existence of weak solutions as well as some regularity and uniqueness properties. Our main result establishes the uniqueness of the trivial solution under some suitable infinity decay conditions for the velocity field only.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76A05 | Non-Newtonian fluids |
| 76U05 | General theory of rotating fluids |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B53 | Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs |
| 35D30 | Weak solutions to PDEs |
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