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arXiv · 2008.12722

Enhanced existence time of solutions to evolution equations of Whitham type

Mats Ehrnström·Yuexun Wang
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Abstract

We show that Whitham type equations u_t + u u_x -L u_x = 0, where L is a general Fourier multiplier operator of order \alpha \in [-1,1], \alpha\neq 0, allow for small solutions to be extended beyond their expected existence time. The result is valid for a range of quadratic dispersive equations with inhomogeneous symbols in the dispersive range given by \alpha, and should be extendable to other equations of the same relative dispersive strength.

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Mats Ehrnström, Yuexun Wang. 2020-08-28. Enhanced existence time of solutions to evolution equations of Whitham type. https://doi.org/10.3934/dcds.2022035

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