ON THE WELL-POSEDNESS OF PARABOLIC EQUATIONS OF NAVIER–STOKES TYPE WITH DATA

Source abstract

We develop a strategy making extensive use of tent spaces to study parabolic equations 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 $\mathbb{R}^{n}$ with small initial data in $\mathit{BMO}^{-1}(\mathbb{R}^{n})$ . We then study another model where neither pointwise kernel bounds nor self-adjointness are available.