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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
J. Málek thanks the Grant Agency of the Czech republic (GACR 201/00/0768) and the Czech Ministry of Education (MSM 113200007) for their support
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Frehse, J., Málek, J. (2003). Problems Due to the No-Slip Boundary in Incompressible Fluid Dynamics. In: Hildebrandt, S., Karcher, H. (eds) Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55627-2_29
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DOI: https://doi.org/10.1007/978-3-642-55627-2_29
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