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

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

doi:10.1007/s00028-021-00752-9

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

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

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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.

Original language	English (US)
Pages (from-to)	5079-5099
Number of pages	21
Journal	Journal of Evolution Equations
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s00028-021-00752-9
State	Published - Dec 2021

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1007/s00028-021-00752-9

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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.\}",

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AU - Dolce, Michele

AU - Feng, Yuanyuan

AU - Mazzucato, Anna L.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85106129394

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JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 4

ER -

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

Abstract

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