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Mixed Boundary Value Problems for Stokes and Navier-Stokes Systems in Polyhedral Domains

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Analysis, Partial Differential Equations and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 193))

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Abstract

The paper deals with a boundary value problem for the stationary Stokes and Navier-Stokes systems, where different boundary conditions (in particular, Dirichlet, Neumann, slip conditions) are prescribed on the faces of a polyhedral domain. Various regularity results in weighted and nonweighted Sobolev and Hölder spaces are given here. Furthermore, the paper contains a maximum modulus estimate for the velocity.

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Authors and Affiliations

  1. Institute of Mathematics, University of Rostock, D-18051, Rostock, Germany

    Jürgen Rossmann

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  1. Jürgen Rossmann
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Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università della Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Alberto Cialdea

  2. Dipartimento di Matematico “Guido Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Paolo Emilio Ricci  & Flavia Lanzara  & 

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Dedicated to Vladimir Maz’ya on the occasion of his 70th birthday

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Rossmann, J. (2009). Mixed Boundary Value Problems for Stokes and Navier-Stokes Systems in Polyhedral Domains. In: Cialdea, A., Ricci, P.E., Lanzara, F. (eds) Analysis, Partial Differential Equations and Applications. Operator Theory: Advances and Applications, vol 193. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9898-9_19

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