Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection

Yuanyuan Feng, Anna L. Mazzucato

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence of mild solutions for arbitrary data in L 2. We then study the issue of global existence. We prove global existence for the KSE in the presence of advection for arbitrary data, provided the advecting velocity field v satisfies certain conditions that ensure the dissipation time of the associated hyperdiffusion-advection equation is sufficiently small. In the absence of advection, global existence can be shown only if the linearized operator does not admit any growing mode and for sufficiently small initial data.

Original languageEnglish (US)
Pages (from-to)279-306
Number of pages28
JournalCommunications in Partial Differential Equations
Issue number2
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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