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

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$$L^2$$${L}^{2}$, using a bootstrap argument. The initial data can be taken arbitrarily large.

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NSF-PAR ID:
10307647
Journal Name:
Journal of Evolution Equations
ISSN:
1424-3199
Publisher:
National Science Foundation
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