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Existence and Regularity of Very Weak Solutions of the Stationary Navier–Stokes Equations

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An Erratum to this article was published on 13 April 2010

Abstract

We consider the stationary Navier–Stokes equations in a bounded domain Ω in R n with smooth connected boundary, where n = 2, 3 or 4. In case that n = 3 or 4, existence of very weak solutions in L n (Ω) is proved for the data belonging to some Sobolev spaces of negative order. Moreover we obtain complete L q-regularity results on very weak solutions in L n (Ω). If n = 2, then similar results are also proved for very weak solutions in \({L^{q_0} (\Omega )}\) with any q 0 > 2. We impose neither smallness conditions on the external force nor boundary data for our existence and regularity results.

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Correspondence to Hyunseok Kim.

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Communicated by C. Le Bris

An erratum to this article can be found at http://dx.doi.org/10.1007/s00205-010-0310-1

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Kim, H. Existence and Regularity of Very Weak Solutions of the Stationary Navier–Stokes Equations. Arch Rational Mech Anal 193, 117–152 (2009). https://doi.org/10.1007/s00205-008-0168-7

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