The Normal Form of the Navier-Stokes Equations in Suitable Normed Spaces

Mots-elés : Navier-Stokes equations, Nonlinear spectral manifolds, Frechet space, Nonresonant spectrum, Parabolic nonlinear equations, Asymptotic expansion,

in Sobolev spaces of sufficiently high order, then we show the existence of a solution in a particular case and finally we solve the general case by using the

There also exists a nonlinear generalized form of the Navier’s conditions.. Fujita has studied the Stokes model with those nonlinear boundary conditions, a well-posed problem leading

In the same way, we obtain here Leray’s weak solutions directly as the incompressible scaling limit of the BGK kinetic model, which is a relaxation model associated with the

TEMAM, Local existence of C~ solutions of the Euler equations of incompressible perfect fluids, in Proc. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis,

NIRENBERG, Partial regularity of suitable weak solutions of the Navier-Stokes equations. FRASCA, Morrey spaces and Hardy-Littlewood maximal

In Section 2, we prove a few orthogonality results concerning the Navier- Stokes equations with profiles as initial data, which will be used in the proof ofTheorem 2.. Section 3

— We proved in Section 2 of [7] a local existence and uniqueness theorem (Theorem 2.2) for solutions of the Navier- Stokes equations with initial data in a space 7-^1 ^2,<5s ^