Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

2019/03/08 by Mingjuan Chen, Boling Guo, Chen, Mingjuan +3
Mathematics · Physics and Astronomy · #35A01 #35Q53 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1903.03291

openalex publication_date 2019/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation ∂_t u-ε∂_x² u+H∂_x²u+u u_x=0, where H denotes the Hilbert transform. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \widetildeH^σ(ℝ)(σ≥ 0), whose low-frequency part is scaling critical and high-frequency part is equal to Sobolev space H^σ(σ≥ 0). Furthermore, we also obtain its inviscid limit behavior in \widetildeH^σ(ℝ)(σ≥ 0).

Citations

• Nonlocal models for nonlinear, dispersive waves
• Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations

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