In this paper, the uniqueness of the solutions to the Navier-Stokesequations in the whole space is constructed, provided that the velocity grows linearly at infinity. The velocity can be chosen as Mx + u(x) for some constant matrix M and some function u. The perturbation u is taken in some homogeneous Besov spaces, which contain some nondecaying functions at space infinity, typically, some almost periodic functions. It is also proved that a locally-in-time solution exists, when M is essentially skew-symmetric which demonstrates the rotating fluid in 2-or 3-dimension.
@article{7484,
title = {The Navier-Stokes flow with linearly growing initial velocity in the whole space - doi: 10.5269/bspm.v22i2.7484},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v22i2.7484},
language = {EN},
url = {http://dml.mathdoc.fr/item/7484}
}
Sawada, Okihiro. The Navier-Stokes flow with linearly growing initial velocity in the whole space - doi: 10.5269/bspm.v22i2.7484. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v22i2.7484. http://gdmltest.u-ga.fr/item/7484/