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

^*Corresponding author for this work

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

18 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
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
Externally published	Yes

Keywords

Diffusion time
Enhanced diffusion
Global existence
Kuramoto–Sivashinsky
Mild solutions
Mixing
Two dimension

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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.",

keywords = "Diffusion time, Enhanced diffusion, Global existence, Kuramoto–Sivashinsky, Mild solutions, Mixing, Two dimension",

author = "\{Coti Zelati\}, Michele and Michele Dolce and Yuanyuan Feng and Mazzucato, \{Anna L.\}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2021",

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doi = "10.1007/s00028-021-00752-9",

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AU - Coti Zelati, Michele

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.

KW - Diffusion time

KW - Enhanced diffusion

KW - Global existence

KW - Kuramoto–Sivashinsky

KW - Mild solutions

KW - Mixing

KW - Two dimension

UR - https://www.scopus.com/pages/publications/85106129394

U2 - 10.1007/s00028-021-00752-9

DO - 10.1007/s00028-021-00752-9

M3 - 文章

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SN - 1424-3199

VL - 21

SP - 5079

EP - 5099

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

Keywords

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