On the regularity of the bilinear term for solutions to the incompressible

Niveau: Supérieur, Licence, Bac+3
On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations Marco Cannone U.F.R. Mathematiques, Universite Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France, e-mail and Fabrice Planchon Program in Applied and Computational Mathematics, Princeton University, Princeton NJ 08544-1000, USA e-mail Abstract We derive various estimates for strong solutions to the Navier- Stokes equations in C([0, T ), L3(R3 )) that allow us to prove some reg- ularity results on the kinematic bilinear term. Introduction and definitions The Cauchy problem for the Navier-Stokes equations governing the time evolution of the velocity u(x, t) = (u1(x, t), u2(x, t), u3(x, t)) and the pressure 1

• besov spaces


• differential operator


• h˙sp ??


• ?? l3


• definition involving


• various estimates


• space variable


• sobolev ones


• reg- ularity results