@article{bc4c95dfb4494c148fc21bb3bb2af92a,
title = "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 L2, using a bootstrap argument. The initial data can be taken arbitrarily large.",
author = "{Coti Zelati}, Michele and Michele Dolce and Yuanyuan Feng and Mazzucato, {Anna L.}",
note = "Funding Information: On behalf of all authors, the corresponding author states that there is no conflict of interest. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. A.M. was partially supported by the US National Science Foundation Grant DMS-1909103. Part of this work was conducted while A.M. participated remotely in a program hosted by the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, during the Spring 2021 semester. MSRI receives major support from the US National Science Foundation under Grant DMS-1928930. M.C.Z. and M.D. acknowledges funding from the Royal Society through a University Research Fellowship (URF/R1/191492) Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
month = dec,
doi = "10.1007/s00028-021-00752-9",
language = "English (US)",
volume = "21",
pages = "5079--5099",
journal = "Journal of Evolution Equations",
issn = "1424-3199",
publisher = "Birkhauser Verlag Basel",
number = "4",
}