On the Large-<i>x</i> Asymptotic of the Classical Solutions to the Non-Linear Benjamin Equation in Fractional Sobolev Spaces
In this work, we study the large-<i>x</i> asymptotic of classical solutions to the non-linear Benjamin equation modeling propagation of small amplitude internal waves in a two fluid system. In our analysis, we extend known <inline-formula><math xmlns="http://www.w3.org/1998...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-10-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/11/635 |
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| Summary: | In this work, we study the large-<i>x</i> asymptotic of classical solutions to the non-linear Benjamin equation modeling propagation of small amplitude internal waves in a two fluid system. In our analysis, we extend known <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>H</mi><mi>s</mi></msup></semantics></math></inline-formula>-well-posedness results to the case of the variable-weight Sobolev spaces. The spaces provide a direct control over the asymptotics of classical solutions and their weak derivatives, and permit us to compute the bulk large-<i>x</i> asymptotic of classical solutions explicitly in terms of input data. The asymptotic formula provides a precise description of the qualitative behaviour of classical solutions in weighted spaces and yields a number of weighted persistence and continuation results automatically. |
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| ISSN: | 2504-3110 |