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A uniform Besov boundedness and the well-posedness of the generalized dissipative quasi-geostrophic equation in the critical Besov space

  • Yanping Chen EMAIL logo , Zihua Guo and Tian Tian
From the journal Forum Mathematicum

Abstract

In this paper, we consider a kind of singular integrals which appear in the generalized 2D dissipative quasi-geostrophic (QG) equation

t θ + u θ + κ Λ 2 β θ = 0 , ( x , t ) 2 × + , κ > 0 ,

where u = - Λ - 2 + 2 α θ , α [ 0 , 1 2 ] and β ( 0 , 1 ] . First, we give a relationship between this kind of singular integrals and Calderón–Zygmund singular integral operators and obtain a uniform Besov estimates. As an application, we give the well-posedness of the generalized 2D dissipative quasi-geostrophic (QG) in the critical Besov space.

MSC 2020: 42B37; 42B20; 35Q35

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 11871096

Award Identifier / Grant number: DP200101065

Funding statement: Yanping Chen was partially supported by the National Natural Science Foundation of China (No. 11871096). Zihua Guo was partially supported by ARC DP200101065.

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Received: 2023-02-14
Revised: 2023-05-05
Published Online: 2023-06-27
Published in Print: 2024-03-01

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