The Navier-Stokes equation in the bidimensional torus is considered, with initial velocity in the Besov spaces B-pr(-s+2-2/r) and forcing term in L-r (0, T; B-pq(-s)) for suitable indices s, r, p, q, Results of local existence and uniqueness are proven in the case -1 < -s + 2 - 2/r < 0 and of global existence in the case -1/2 < -s + 2 - 2/r < 0. (C) 2008 Elsevier Ltd. All rights reserved.
- Navier-Stokes equations
- Weak solutions
- Existence uniqueness and regularity theory