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Problems Due to the No-Slip Boundary in Incompressible Fluid Dynamics

In: Geometric Analysis and Nonlinear Partial Differential Equations

Author

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  • Jens Frehse

    (Universität Bonn, Institut für Angewandte Mathematik)

  • Josef Málek

    (Mathematical Institute of Charles University)

Abstract

Summary Dealing with the analysis of the systems of PDE’s describing unsteady flows of incompressible fluids, we focus on open problems that occur if the equations are supplemented by the homogeneous Dirichlet (no-slip) boundary conditions, but that are successfully solvable in the spatially periodic setting, for example. Within this framework we also present four different approaches to obtain compactness of weakly converging quantities and discuss how these tools can be used in the global existence theory for the power-law fluids and their various generalizations.

Suggested Citation

  • Jens Frehse & Josef Málek, 2003. "Problems Due to the No-Slip Boundary in Incompressible Fluid Dynamics," Springer Books, in: Stefan Hildebrandt & Hermann Karcher (ed.), Geometric Analysis and Nonlinear Partial Differential Equations, pages 559-571, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55627-2_29
    DOI: 10.1007/978-3-642-55627-2_29
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