On well-posedness of parabolic equations of Navier-Stokes type with BMO^{-1}(\R^n) data

Abstract

We 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.

Second revision. Addition of 9 pages. Statement and proof of a corresponding linear PDE and proofs that we obtain indeed weak solutions