Large-time behaviour of solutions to the surface quasi-geostrophic equation

Dáithí Ó hAodha; Tsukasa Iwabuchi

doi:10.1007/s42985-022-00197-w

Large-time behaviour of solutions to the surface quasi-geostrophic equation

Dáithí Ó hAodha, Tsukasa Iwabuchi

SCI - Mathematics

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

Abstract

We construct a linear approximation of the solution to the surface quasi-geostrophic equation in 2-dimensional Euclidean space, and obtain a convergence rate in the Lebesgue norm between the solution and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution is bounded sharply by the same function of time.

Original language	English
Article number	60
Journal	Partial Differential Equations and Applications
Volume	3
Issue number	5
DOIs	https://doi.org/10.1007/s42985-022-00197-w
Publication status	Published - 2022 Oct

Keywords

Fractional Laplacian
Large-time behaviour
Linear approximation
Quasi-geostrophic
Sharp estimate

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1007/s42985-022-00197-w

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title = "Large-time behaviour of solutions to the surface quasi-geostrophic equation",

abstract = "We construct a linear approximation of the solution to the surface quasi-geostrophic equation in 2-dimensional Euclidean space, and obtain a convergence rate in the Lebesgue norm between the solution and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution is bounded sharply by the same function of time.",

keywords = "Fractional Laplacian, Large-time behaviour, Linear approximation, Quasi-geostrophic, Sharp estimate",

author = "{{\'O} hAodha}, D{\'a}ith{\'i} and Tsukasa Iwabuchi",

note = "Funding Information: T. Iwabuchi was supported by JSPS Grant-in-Aid for Young Scientists (A) (No. 17H04824). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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doi = "10.1007/s42985-022-00197-w",

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TY - JOUR

T1 - Large-time behaviour of solutions to the surface quasi-geostrophic equation

AU - Ó hAodha, Dáithí

AU - Iwabuchi, Tsukasa

N1 - Funding Information: T. Iwabuchi was supported by JSPS Grant-in-Aid for Young Scientists (A) (No. 17H04824). Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/10

Y1 - 2022/10

N2 - We construct a linear approximation of the solution to the surface quasi-geostrophic equation in 2-dimensional Euclidean space, and obtain a convergence rate in the Lebesgue norm between the solution and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution is bounded sharply by the same function of time.

AB - We construct a linear approximation of the solution to the surface quasi-geostrophic equation in 2-dimensional Euclidean space, and obtain a convergence rate in the Lebesgue norm between the solution and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution is bounded sharply by the same function of time.

KW - Fractional Laplacian

KW - Large-time behaviour

KW - Linear approximation

KW - Quasi-geostrophic

KW - Sharp estimate

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VL - 3

JO - Partial Differential Equations and Applications

JF - Partial Differential Equations and Applications

IS - 5

M1 - 60

ER -

Large-time behaviour of solutions to the surface quasi-geostrophic equation

Abstract

Keywords

ASJC Scopus subject areas

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