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We develop a strategy making extensive use of tent spaces to study parabolicequa-tions with quadratic nonlinearities as for the Navier-Stokes system. Webegin with a new proof of the well-known result of Koch and Tataru on thewell-posedness of Navier-Stokes equations in \R^n with small initial data inBMO^{-1}(\R^n). We then study another model where neither pointwise kernelbounds nor self-adjointness are available.

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