A priori bounds and equicontinuity of orbits for the intermediate long wave equation

article A priori bounds and equicontinuity of orbits for the intermediate long wave equation published yes B. Harrop-Griffiths author R. Killip author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca We prove uniform-in-time a priori Hs bounds for solutions to the intermediate longwave equation posed both on the line and on the circle, covering the range −1 2 < s ≤ 0. Additionally, we prove that the set of orbits emanating from a bounded and equicontinuous set in Hs is also bounded and equicontinuous in Hs . Our proof is based on the identification of a suitable Lax pair formulation for the intermediate long wave equation. Springer Nature2026 eng Journal of Evolution Equations 1424-3199 1424-3202 2506.2386810.1007/s00028-026-01228-4 263 yes Harrop-Griffiths B, Killip R, Vişan M. A priori bounds and equicontinuity of orbits for the intermediate long wave equation. Journal of Evolution Equations. 2026;26(3). doi:<a href="https://doi.org/10.1007/s00028-026-01228-4">10.1007/s00028-026-01228-4</a> Harrop-Griffiths, B., et al. “A Priori Bounds and Equicontinuity of Orbits for the Intermediate Long Wave Equation.” Journal of Evolution Equations, vol. 26, no. 3, 81, Springer Nature, 2026, doi:<a href="https://doi.org/10.1007/s00028-026-01228-4">10.1007/s00028-026-01228-4</a>. B. Harrop-Griffiths, R. Killip, M. Vişan, Journal of Evolution Equations 26 (2026). Harrop-Griffiths B, Killip R, Vişan M. 2026. A priori bounds and equicontinuity of orbits for the intermediate long wave equation. Journal of Evolution Equations. 26(3), 81. Harrop-Griffiths, B., R. Killip, and Monica Vişan. “A Priori Bounds and Equicontinuity of Orbits for the Intermediate Long Wave Equation.” Journal of Evolution Equations. Springer Nature, 2026. <a href="https://doi.org/10.1007/s00028-026-01228-4">https://doi.org/10.1007/s00028-026-01228-4</a>. B. Harrop-Griffiths, R. Killip, and M. Vişan, “A priori bounds and equicontinuity of orbits for the intermediate long wave equation,” Journal of Evolution Equations, vol. 26, no. 3. Springer Nature, 2026. Harrop-Griffiths, B., Killip, R., & Vişan, M. (2026). A priori bounds and equicontinuity of orbits for the intermediate long wave equation. Journal of Evolution Equations. Springer Nature. <a href="https://doi.org/10.1007/s00028-026-01228-4">https://doi.org/10.1007/s00028-026-01228-4</a> 220962026-06-19T08:58:33Z2026-07-02T06:02:36Z