## The normal form of the Navier-Stokes equations in suitable normed spaces.(English)Zbl 1179.35212

The authors consider the 3D incompressible Navier-Stokes system (NS) on the torus $$\Omega=[0,2\pi]^3$$ with given body forces. They consider the set $${\mathcal R}\subset H^1(\Omega)$$ of initial data for which there exists a regular solution of (NS) and they construct a Banach space $$S_A^*$$ such that the normalization map $$W : {\mathcal R}\rightarrow S_A^*$$ is continuous and such that the normal form of (NS) is well-posed in $$S_A^*$$. They prove that $$S_A^*$$ is a subset of a Banach space $$V^*$$ such that the extended Navier-Stokes system is well-posed in $$V^*$$.

### MSC:

 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 46N20 Applications of functional analysis to differential and integral equations
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### References:

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