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

Jens Frehse and Josef Málek
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Jens Frehse: Universität Bonn, Institut für Angewandte Mathematik
Josef Málek: Mathematical Institute of Charles University

A chapter in Geometric Analysis and Nonlinear Partial Differential Equations, 2003, pp 559-571 from Springer

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.

Keywords: Weak Solution; Incompressible Fluid; Lipschitz Approximation; Shear Dependent Viscosity; Suitable Test Function (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55627-2_29

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DOI: 10.1007/978-3-642-55627-2_29

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