Global attractor for weakly damped, forced mKdV equation in low regularity spaces

Goyal, Prashant

doi:10.1007/s40863-020-00207-y

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Ryan Mcconnell1

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2023

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“…Later, Erdogan and Tzirakis showed in [11] using smoothing that (2) has a global attractor in L2 that is compact in H s , s ∈ (0, 1), with forcing in L2 . Moving on to the mKdV, Goyal [16] proved an analogous statement to those of Tsugawa and Yang by proving that the forced and damped mKdV possesses a global attractor in Ḣs for 1 > s > 11/12 with forcing f ∈ L2 ∩ H 1 , later improved to 1 > s > 9/10 in [17].…”

Section: Ryan Mcconnellmentioning

confidence: 72%

Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

McConnell

2023

DCDS-B

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<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ H^1 $\end{document}</tex-math></inline-formula>. As a consequence, we establish the existence of a global attractor for this equation as well as its compactness in <inline-formula><tex-math id="M2">\begin{document}$ H^s(\mathbb{T}) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ s\in (1, 2). $\end{document}</tex-math></inline-formula></p>

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Section: Ryan Mcconnellmentioning

confidence: 72%

Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

McConnell

2023

DCDS-B

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Global attractor for weakly damped, forced mKdV equation in low regularity spaces

Cited by 1 publication

References 24 publications

Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

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