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On the Stokes and Oseen Problems with Singular Data

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Abstract

We consider the steady Stokes and Oseen problems in bounded and exterior domains of \({\mathbb{R}^n}\) of class C k-1,1 (n = 2, 3; k ≥ 2). We prove existence and uniqueness of a very weak solution for boundary data a in \({W^{2-k-1/q,q} (\partial\Omega)}\) . If \({\Omega}\) is of class \({C^\infty}\) , we can assume a to be a distribution on \({\partial\Omega}\) .

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Authors and Affiliations

  1. Department of Mathematics and Physics, Second University of Naples, Viale Lincoln 5, 81100, Caserta, Italy

    Alfonsina Tartaglione

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  1. Alfonsina Tartaglione
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Correspondence to Alfonsina Tartaglione.

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Communicated by G.P. Galdi

This work was partially supported by Istituto Nazionale di Alta Matematica “F. Severi”.

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Tartaglione, A. On the Stokes and Oseen Problems with Singular Data. J. Math. Fluid Mech. 16, 407–417 (2014). https://doi.org/10.1007/s00021-013-0161-2

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