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arXiv · 2105.13405

Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing

Ryan McConnell
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Abstract

We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial non-linearity, damping, and forcing that matches the smoothing level for the gKdV at $H^1$. As a consequence, we establish the existence of a global attractor for this equation as well as its compactness in $H^s(\mathbb{T})$, $s\in (1,2).$

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Ryan McConnell. 2021-05-26. Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing. https://arxiv.org/abs/2105.13405

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