Global existence and exponential stability for the micropolar fluid system. (English) Zbl 1155.76009

Villamizar-Roa, Elder Jesús; Rodríguez-Bellido, María Ángeles

Z. Angew. Math. Phys. 59, No. 5, 790-809 (2008).

Summary: We consider the micropolar fluid system in a bounded domain of \(\mathbb{R}^{3}\) and prove the existence and uniqueness of a global strong solution with initial data being a perturbation of stationary solution, whose existence is also obtained. We prove that these solutions converge uniformly to stationary solutions with exponential decay rate. The technique of our analysis is the semigroup approach in \(L^{p}\)-spaces.

MSC:

76A05	Non-Newtonian fluids
35Q35	PDEs in connection with fluid mechanics

Keywords:

strong solution; perturbed stationary solution; semigroup approach