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arXiv · 1412.8407

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

Pascal Auscher·Dorothee Frey
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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.

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Pascal Auscher, Dorothee Frey. 2014-12-29. On well-posedness of parabolic equations of Navier-Stokes type with BMO^{-1}(\R^n) data. https://arxiv.org/abs/1412.8407

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