Document Type
Article
Publication Date
7-10-2013
Abstract
We show the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces belonging to a critical space. To the best of our knowledge, this is the largest critical space that is available up until now for this kind of existence. This result can be viewed as the stationary counterpart of the existence result obtained by H.Koch and D.Tataru for the free non-stationary Navier-Stokes equations with initial data in BMO -1. The stability of the stationary solutions in such spaces is also obtained by a series of sharp estimates for resolvents of a singularly perturbed operator and the corresponding semigroup. © 2013 Elsevier Ltd.
Publication Source (Journal or Book title)
Advances in Mathematics
First Page
137
Last Page
161
Recommended Citation
Phan, T., & Phuc, N. (2013). Stationary Navier-Stokes equations with critically singular external forces: Existence and stability results. Advances in Mathematics, 241, 137-161. https://doi.org/10.1016/j.aim.2013.01.016