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The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains

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Abstract.

We consider the linearized version of the stationary Navier-Stokes equations on a subdomain Ω of a smooth, compact Riemannian manifold M. The emphasis is on regularity: the boundary of Ω is assumed to be only C1 and even Lipschitz, and the data are selected from appropriate Sobolev-Besov scales. Our approach relies on the method of boundary integral equations, suitably adapted to the variable-coefficient setting we are considering here. Applications to the stationary, nonlinear Navier-Stokes equations in this context are also discussed.

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Acknowledgements.

We are grateful to MICHAEL TAYLOR for his interest in our work and for his support over the years. We also thank the editor and the referees for their constructive criticism. Their comments and suggestions have led to the present version of the paper. MARIUS MITREA was partly supported by NSF and a University of Missouri Research Board Grant.

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Dindoŝ, M., Mitrea, M. The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains. Arch. Rational Mech. Anal. 174, 1–47 (2004). https://doi.org/10.1007/s00205-004-0320-y

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