2021/03/31 by Xiangqian Yan, Wei Yan, Yan, Xiangqian +1
Mathematics · Physics and Astronomy · #35G25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35G25
paper · pdf · doi:10.48550/arxiv.2104.00549
arxiv created 2021/03/31 · openalex publication_date 2021/03/31 · arxiv updated 2021/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to studying the Cauchy problem for the generalized Ostrovsky equation ut-β∂x3u-γ∂x-1u+(1)/(k+1)(uk+1)x=0,k≥5 with βγ<0,γ>0. Firstly, we prove that the Cauchy problem for the generalized Ostrovsky equation is locally well-posed in Hs(ℝ)(s>(1)/(2)-(2)/(k)). Then, we prove that the Cauchy problem for the generalized Ostrovsky equation is locally well-posed in Xs(ℝ): =‖f‖Hs+‖\mathscrFx-1(\frac\mathscrFx f(ξ)ξ)‖Hs(s>(1)/(2)-(2)/(k)). Finally, we show that the solution to the Cauchy problem for generalized Ostrovsky equation converges to the solution to the generalized KdV equation as the rotation parameter γ tends to zero for data belonging to Xs(ℝ)(s>(3)/(2)). The main difficulty is that the phase function of Ostrosvky equation with negative dispersive βξ3+\fracγξ possesses the zero singular point.