<b>The Navier-Stokes flow with linearly growing initial velocity in the whole space</b> - doi: 10.5269/bspm.v22i2.7484

Résumé

In this paper, the uniqueness of the solutions to the Navier-Stokes
equations 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.