Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method

2013/01/09 by John K. Hunter, Mihaela Ifrim, Hunter, John K. +5 · 3 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1301.1947

openalex publication_date 2013/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a modified energy method to prove the existence of small, smooth solutions over cubically nonlinear time-scales.

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