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 \(V^*\).


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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