abstract: In papers 1 and 2, it is considered the interesting question of non decaying solutions to the Navier-Stokes Cauchy problem in the two dimensional case. The existence concerns regular solutions defined for all t > 0. In paper 3, it is considered the Navier-Stokes initial boundary value problem in a two dimensional exterior domain Ω under the assumption of an initial data u0 in BUC (Ω) with \nabla u0 ∈ L∞(Ω). We establish global existence and uniqueness of regular solutions.
1 Y. Giga, S. Matsui and O. Sawada, J. math. fluid mech., 3 (2001), 302-315.
2 O. Sawada and Y. Taniuchi, J. math. fluid mech., 9 (2007), 533-542.
3 P. Maremonti and S. Shimizu, Global existence of solutions to 2-D Navier-Stokes flow with non decaying initial data in exterior domains, submitted.