Global existence for the two-dimensional Kuramoto–Sivashinsky equation with a shear flow

Michele Coti Zelati, Michele Dolce, Yuanyuan Feng, Anna L. Mazzucato

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We consider the Kuramoto–Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow. Under the assumption that the shear has a finite number of critical points and there are linearly growing modes only in the direction of the shear, we prove global existence of solutions with data in L2, using a bootstrap argument. The initial data can be taken arbitrarily large.

Original languageEnglish (US)
Pages (from-to)5079-5099
Number of pages21
JournalJournal of Evolution Equations
Issue number4
StatePublished - Dec 2021

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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