Wyniki wyszukiwania

1

Global mild solutions of the micropolar fluid system in critical spaces

100%

Xu F., Yuan J.

Applicationes Mathematicae

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2013

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tom 40

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nr 1

21-29

EN

We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.

2

Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces

100%

Wu G., Yuan J.

Applicationes Mathematicae

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2007

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tom 34

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nr 3

253-267

EN

We study local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation $∂_{t}u - ∂³_{txx}u + 2κ∂_{x}u + ∂_{x}[g(u)/2] = γ(2∂_{x}u∂²_{xx}u + u∂³_{xxx}u)$ for the initial data u₀(x) in the Besov space $B^{s}_{p,r}(ℝ)$ with max(3/2,1 + 1/p) < s ≤ m and (p,r) ∈ [1,∞]², where g:ℝ → ℝ is a given $C^{m}$-function (m ≥ 4) with g(0)=g'(0)=0, and κ ≥ 0 and γ ∈ ℝ are fixed constants. Using estimates for the transport equation in the framework of Besov spaces, compactness arguments and Littlewood-Paley theory, we get a local well-posedness result.

3

Logarithmically improved regularity criteria for the micropolar fluid equations

81%

Xu F., Xu X., Yuan J.

Applicationes Mathematicae

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2012

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tom 39

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nr 3

315-328

EN

We discuss the 3D incompressible micropolar fluid equations, and give logarithmically improved regularity criteria in terms of both the velocity field and the pressure in Morrey-Campanato spaces, BMO spaces and Besov spaces.

Ograniczanie wyników

3 Applicationes Mathematicae

3 Yuan J.

2 Xu F.

1 Wu G.

1 Xu X.

1 2013

1 2012

1 2007

Global mild solutions of the micropolar fluid system in critical spaces

Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces

Logarithmically improved regularity criteria for the micropolar fluid equations