A new proof for Koch and Tataru's result on the well-posedness of Navier-Stokes equations in $BMO^{-1}$

Pascal Auscher (1) , Dorothee Frey (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 MSI - Mathematical Sciences Institute

We give a new proof of a well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in $\R^n$ with small initial data in $BMO^{-1}(\R^n)$. The proof is formulated operator theoretically and does not make use of self-adjointness of the Laplacian.

Mots clés: Hardy spaces; Navier-Stokes equations; tent spaces; maximal regularity; Hardy spaces.

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Pascal Auscher, Dorothee Frey. A new proof for Koch and Tataru's result on the well-posedness of Navier-Stokes equations in $BMO^{-1}$. 2013. ⟨hal-00872813⟩