On the backwards behavior of the solutions of the 2D periodic viscous Camassa-Holm equations (Q5957843)
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scientific article; zbMATH DE number 1719158
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the backwards behavior of the solutions of the 2D periodic viscous Camassa-Holm equations |
scientific article; zbMATH DE number 1719158 |
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On the backwards behavior of the solutions of the 2D periodic viscous Camassa-Holm equations (English)
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13 March 2002
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The author studies the global behavior of periodic two-dimensional viscous Camassa-Holm equations. First, energy and enstrophy balance equations are derived, and it is shown how to control vorticity quotients of the solutions of Camassa-Holm equations by controlling the energy of the solutions from below. Then the author constructs a set of initial data for which the solution exists for all negative times and grows backwards with an exponential rate. This set is proven to be dense in a Hilbert space related to vector-valued divergence-free trigonometric polynomials.
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periodic two-dimensional viscous Camassa-Holm equations
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energy
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enstrophy
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vorticity quotients
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initial data
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Hilbert space
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vector-valued divergence-free trigonometric polynomials
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