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arXiv:1412.8407 [math.AP]AbstractReferencesReviewsResources

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

Pascal Auscher, Dorothee Frey

Published 2014-12-29, updated 2015-04-14Version 3

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.

Comments: Second revision. Addition of 9 pages. Statement and proof of a corresponding linear PDE and proofs that we obtain indeed weak solutions
Categories: math.AP
Subjects: 35Q10, 76D05, 42B37, 42B35
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