Equations Paraboliques de type Navier-Stokes avec données dans $BMO^{-1}$

International audienceWe develop a strategy making extensive use of tent spaces to study parabolic equa-tions with quadratic nonlinearities as for the Navier-Stokes system. We begin with a new proof of the well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in $R^n$ with small initial data in $BMO ^{−1} (R^n)$. We then study another model where neither pointwise kernel bounds nor self-adjointness are available. In this case, $BMO^{−1} (R^n)$ has to be replaced by an adapted space