The IVP for the Kuramoto-Sivashinsky equation in low regularity Sobolev spaces

2019/03/07 by Alysson Cunha, Cunha, Alysson, Eduardo Alarcón +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.02670

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

Abstract

In this work, we study the initial-value problem associated with the Kuramoto-Sivashinsky equation. We show that the associated initial value problem is locally and globally well-posed in Sobolev spaces H^s(ℝ), where s>1/2. We also show that our result is sharp, in the sense that the flow-map data-solution is not C² at origin, for s<1/2. Furthermore, we study the behavior of the solutions when μ\downarrow 0.

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