On well-posedness of parabolic equations of Navier-Stokes type with BMO^-1(\Rⁿ) data

2014/12/29 by Auscher, Pascal, Frey, Dorothee
#35Q10 #42B35 #42B37 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.8407

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 \Rⁿ with small initial data in BMO^-1(\Rⁿ). We then study another model where neither pointwise kernel bounds nor self-adjointness are available.

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