Global Well-Posedness for the Fifth-Order KdV Equation in H- 1(R)

Bjoern Bringmann; Rowan Killip; Monica Visan

doi:10.1007/s40818-021-00111-4

Global Well-Posedness for the Fifth-Order KdV Equation in H^{- 1}(R)

Bjoern Bringmann, Rowan Killip, Monica Visan

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17 Scopus citations

Abstract

We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in H^{- 1}(R). Global well-posedness in L²(R) was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp L² threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.

Original language	English (US)
Article number	21
Journal	Annals of PDE
Volume	7
Issue number	2
DOIs	https://doi.org/10.1007/s40818-021-00111-4
State	Published - Dec 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Geometry and Topology
Mathematical Physics
General Physics and Astronomy

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10.1007/s40818-021-00111-4

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abstract = "We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in H- 1(R). Global well-posedness in L2(R) was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp L2 threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.",

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AU - Killip, Rowan

AU - Visan, Monica

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AB - We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in H- 1(R). Global well-posedness in L2(R) was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp L2 threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.

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Global Well-Posedness for the Fifth-Order KdV Equation in H^{- 1}(R)

Abstract

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