article Global well-posedness for the fifth-order KdV equation in H^-1(R) published yes Bjoern Bringmann author Rowan Killip author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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. Springer Nature2021 eng Annals of PDE 2524-5317 2199-2576 1912.0153610.1007/s40818-021-00111-4 72 yes B. Bringmann, R. Killip, M. Vişan, Annals of PDE 7 (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).” <i>Annals of PDE</i>, vol. 7, no. 2, 21, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s40818-021-00111-4">10.1007/s40818-021-00111-4</a>. Bringmann B, Killip R, Vişan M. Global well-posedness for the fifth-order KdV equation in H^-1(R). <i>Annals of PDE</i>. 2021;7(2). doi:<a href="https://doi.org/10.1007/s40818-021-00111-4">10.1007/s40818-021-00111-4</a> Bringmann, B., Killip, R., &#38; Vişan, M. (2021). Global well-posedness for the fifth-order KdV equation in H^-1(R). <i>Annals of PDE</i>. Springer Nature. <a href="https://doi.org/10.1007/s40818-021-00111-4">https://doi.org/10.1007/s40818-021-00111-4</a> B. Bringmann, R. Killip, and M. Vişan, “Global well-posedness for the fifth-order KdV equation in H^-1(R),” <i>Annals of PDE</i>, vol. 7, no. 2. Springer Nature, 2021. Bringmann, Bjoern, Rowan Killip, and Monica Vişan. “Global Well-Posedness for the Fifth-Order KdV Equation in H^-1(R).” <i>Annals of PDE</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s40818-021-00111-4">https://doi.org/10.1007/s40818-021-00111-4</a>. 220382026-06-19T07:44:49Z2026-06-22T13:03:48Z