It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.
We consider the Kuramoto–Sivashinsky equation (KSE) on the twodimensional 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
 Publication Date:
 NSFPAR ID:
 10307647
 Journal Name:
 Journal of Evolution Equations
 ISSN:
 14243199
 Publisher:
 Springer Science + Business Media
 Sponsoring Org:
 National Science Foundation
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