The third order Benjamin-Ono equation on the torus : well-posedness, traveling waves and stability

2019/12/17 by Louise Gassot, Gassot, Louise
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1912.07903

openalex publication_date 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the third order Benjamin-Ono equation on the torus ∂_t u= ∂_x ( -∂_xxu-(3)/(2)u H∂_x u - (3)/(2)H(u∂_x u) + u³ ). We prove that for any t∈ℝ, the flow map continuously extends to H^s_r,0(\mathbbT) if s≥ 0, but does not admit a continuous extension to H^-s_r,0(\mathbbT) if 0

Citations

• Local well-posedness for fourth order Benjamin-Ono type equations
• On the integrability of the Benjamin-Ono equation on the torus
• On the flow map of the Benjamin-Ono equation on the torus

Related

• On the flow map of the Benjamin-Ono equation on the torus
• Local well-posedness for third order Benjamin-Ono type equations on the torus
• Sharp well-posedness results of the Benjamin-Ono equation in H^s(\mathbbT,ℝ) and qualitative properties of its solution
• Long time behavior of solutions for a damped Benjamin-Ono equation
• Invariant measures and long time behaviour for the Benjamin-Ono equation