On the Blowup for the 3D Axisymmetric Incompressible Chemotaxis-Euler Equations

Journal of Function Spaces ◽

10.1155/2021/5541713 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Shangyong An ◽

Qian Zhang

Keyword(s):

Euler Equations ◽

Localization Method ◽

Blowup Criterion ◽

Fourier Localization

In this paper, we investigate the 3D incompressible chemotaxis-Euler equations. Taking advantage of the structure of axisymmetric fluids, we establish the blowup criterion of the system using the Fourier localization method.

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Local existence and blowup criterion of the Lagrangian averaged Euler equations in Besov spaces

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2008.7.845 ◽

2008 ◽

Vol 7 (4) ◽

pp. 845-852 ◽

Cited By ~ 4

Author(s):

Houyu Jia ◽

◽

Xiaofeng Liu ◽

Keyword(s):

Euler Equations ◽

Besov Spaces ◽

Local Existence ◽

Blowup Criterion

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Blowup criterion of smooth solutions for the incompressible chemotaxis-Euler equations

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.201500040 ◽

2015 ◽

Vol 96 (4) ◽

pp. 466-476 ◽

Cited By ~ 1

Author(s):

Qian Zhang

Keyword(s):

Euler Equations ◽

Smooth Solutions ◽

Blowup Criterion

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Local existence and blowup criterion for the Euler equations in a function space with nondecaying derivatives

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125068 ◽

2021 ◽

Vol 500 (1) ◽

pp. 125068

Author(s):

Daisuke Hirata

Keyword(s):

Function Space ◽

Euler Equations ◽

Local Existence ◽

Blowup Criterion

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Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

Moroccan Journal of Pure and Applied Analysis ◽

10.1515/mjpaa-2017-0001 ◽

2017 ◽

Vol 3 (1) ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Azzeddine El Baraka ◽

Mohamed Toumlilin

Keyword(s):

Cauchy Problem ◽

Stokes Equations ◽

Morrey Spaces ◽

Navier Stokes ◽

Well Posedness ◽

Navier Stokes Equations ◽

Small Initial Data ◽

Localization Method ◽

Fourier Localization ◽

The Cauchy Problem

Abstract In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].

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