2025-12-302025-12-302026CUNHA, Alysson. Improvement of the parabolic regularization method and applications to dispersive models. Nonlinear Analysis, Amsterdam, v. 263, e113964, 2026. DOI: 10.1016/j.na.2025.113964. Disponível em: https://www.sciencedirect.com/science/article/pii/S0362546X25002160?dgcid=rss_sd_all. Acesso em: 8 dez. 2025.0362-546Xe- 1873-5215https://www.sciencedirect.com/science/article/pii/S0362546X25002160?dgcid=rss_sd_allWe prove that the Benjamin–Ono equation is globally well-posed in for . Our approach does not rely on the global gauge transformation introduced by Tao (Tao, 2004). Instead, we employ a modified version of the standard parabolic regularization method. In particular, this technique also enables us to establish global well-posedness, in the same Sobolev space, for the dispersion-generalized Benjamin–Ono (DGBO) equation.engAcesso RestritoBO equationDGBO equationInitial-value problemWell-posednessSobolev spacesArtigo10.1016/j.na.2025.113964