On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations
Copyright policy )On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations
Summary: A compactness proof of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations is presented. The compactness of the operator provides important information for fixed-point formulations, especially for computer-assisted proofs based on Schauder's fixed-point theorem. Our idea for the compactness proof comes from books by \textit{V. Girault} and \textit{P.-A. Raviart} [Finite element methods for Navier-Stokes equations. Theory and algorithms. (Extended version of the 1979 publ.). Berlin etc.: Springer (1986; Zbl 0585.65077)] and \textit{O. A. Ladyzhenskaya} [The mathematical theory of viscous incompressible flow. Translated from the Russian by R. A. Silverman. New York-London: Gordon and Breach Science Publishers (1963; Zbl 0121.42701)], and our principle would be also applied to convex polygonal regions.
- Kyushu University Japan
- Waseda University Japan
- Karlsruhe Institute of Technology Germany
- Karlsruhe Institute of Technology / KIT Germany
Boundary value problems for higher-order elliptic equations, Schauder's fixed-point theorem, General theory of partial differential operators, Multilinear and polynomial operators, fixed-point formulations, Pseudodifferential operators, Navier-Stokes equations, convex polygonal regions, Topological and monotonicity methods applied to PDEs
Boundary value problems for higher-order elliptic equations, Schauder's fixed-point theorem, General theory of partial differential operators, Multilinear and polynomial operators, fixed-point formulations, Pseudodifferential operators, Navier-Stokes equations, convex polygonal regions, Topological and monotonicity methods applied to PDEs
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