Global well-posedness for the fifth-order KdV equation in H^-1(R)
Bringmann B, Killip R, Vişan M. 2021. Global well-posedness for the fifth-order KdV equation in H^-1(R). Annals of PDE. 7(2), 21.
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Author
Bringmann, Bjoern;
Killip, Rowan;
Vişan, MonicaISTA
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 L^2(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 L^2 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.
Publishing Year
Date Published
2021-08-25
Journal Title
Annals of PDE
Publisher
Springer Nature
Volume
7
Issue
2
Article Number
21
ISSN
eISSN
IST-REx-ID
Cite this
Bringmann B, Killip R, Vişan M. Global well-posedness for the fifth-order KdV equation in H^-1(R). Annals of PDE. 2021;7(2). doi:10.1007/s40818-021-00111-4
Bringmann, B., Killip, R., & Vişan, M. (2021). Global well-posedness for the fifth-order KdV equation in H^-1(R). Annals of PDE. Springer Nature. https://doi.org/10.1007/s40818-021-00111-4
Bringmann, Bjoern, Rowan Killip, and Monica Vişan. “Global Well-Posedness for the Fifth-Order KdV Equation in H^-1(R).” Annals of PDE. Springer Nature, 2021. https://doi.org/10.1007/s40818-021-00111-4.
B. Bringmann, R. Killip, and M. Vişan, “Global well-posedness for the fifth-order KdV equation in H^-1(R),” Annals of PDE, vol. 7, no. 2. Springer Nature, 2021.
Bringmann B, Killip R, Vişan M. 2021. Global well-posedness for the fifth-order KdV equation in H^-1(R). Annals of PDE. 7(2), 21.
Bringmann, Bjoern, et al. “Global Well-Posedness for the Fifth-Order KdV Equation in H^-1(R).” Annals of PDE, vol. 7, no. 2, 21, Springer Nature, 2021, doi:10.1007/s40818-021-00111-4.
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