Flow-invariant closed sets with respect to nonlinear semigroup flows (Q1402439)
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scientific article; zbMATH DE number 1971897
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Flow-invariant closed sets with respect to nonlinear semigroup flows |
scientific article; zbMATH DE number 1971897 |
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Flow-invariant closed sets with respect to nonlinear semigroup flows (English)
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27 August 2003
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A necessary and sufficient condition is given for the flow-invariance of a closed set of a Banach space with respect to a differential equation involving a nonlinear semigroup generator in the sense of the Crandall-Ligett formula. The abstract result is applied to study the flow-invariant sets for semilinear parabolic equations. Other applications concern the flow-invariance of the enstrophy and helicity sets in the setting of Navier-Stokes equations.
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Crandall-Ligett formula
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nonlinear semigroup generators
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semilinear parabolic equations
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