共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, the Cauchy problem for the 3D micropolar fluid equations is investigated. A new logarithmically improved blow-up criterion for the 3D micropolar fluid equations in an appropriate homogeneous Besov space is established. 相似文献
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Bo-Qing Dong Wenliang Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2334-1953
This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. When the velocity field satisfies for −1<r<1, then the weak solution (u,w) is regular on (0,T]. The methods are mainly based on the Fourier localization technique and Bony’s para-product decomposition. 相似文献
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In this work, we prove a regularity criterion for micropolar fluid flows in terms of the pressure in Besov space. 相似文献
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This paper is investigate the regularity criteria of weak solutions to the three-dimensional microp- olar fluid equations. Several sufficient conditions in terms of some partial derivatives of the velocity or the pressure are obtained. 相似文献
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Piotr Szopa 《Journal of Mathematical Analysis and Applications》2009,351(1):340-1595
In this paper we consider the solutions of micropolar fluid equations in space dimension two with periodic boundary condition. We show that the strong solutions are analytic in time with values in an appropriate Gevrey class of function, provided that external forces and moments are time-independent and are in a Gevrey class. 相似文献
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Two Regularity Criteria Via the Logarithm of the Weak Solutions to the Micropolar Fluid Equations
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Sadek Gala & Jia Yan 《偏微分方程(英文版)》2012,25(1):32-40
In this note, a logarithmic improved regularity criteria for the micropolar fluid equations are established in terms of the velocity field or the pressure in the homogeneous Besov space. 相似文献
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This paper is devoted to the global in time existence of classical solutions to the d-Dimensional (dD) micropolar equations with fractional dissipation. Micropolar equations model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium. It remains unknown whether or not smooth solutions of the classical 3D micropolar equations can develop finite-time singularities. The purpose here is to explore the global regularity of solutions for dD micropolar equations under the smallest amount of dissipation. We establish the global regularity for two important fractional dissipation cases. Direct energy estimates are not sufficient to obtain the desired global a priori bounds in each case. To overcome the difficulties, we employ the Besov space techniques. 相似文献
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The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces
Zhaoyin Xiang 《Mathematical Methods in the Applied Sciences》2011,34(3):360-372
In this paper, by using the Fourier localization technique and Bony's paraproduct decomposition, we give a regularity criterion of the weak solution to 3D viscous Boussinesq equations in Besov spaces. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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In this paper we prove the global existence and uniqueness of smooth solutions to the 2D micropolar fluid flows with zero angular viscosity. 相似文献
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This article proves the logarithmically improved Serrin's criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] (Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806–808) and [18] (Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375: 799–802). 相似文献
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利用解析性估计和方程非线性项的特殊结构,本文证明了三维各向异Navier-Stokes方程对一类在垂直方向慢变的大初值的整体适定性. 相似文献
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This paper concerns with a regularity criterion of solutions to the 2D dissipative quasi-geostrophic equations. Based on a logarithmic Sobolev inequality in Besov spaces, the absence of singularities of θ in [0,T] is derived for θ a solution on the interval [0,T) satisfying the condition
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We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])). 相似文献
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Huiling Duan 《Applicable analysis》2013,92(5):947-952
In this article, we consider regularity of solutions to the 3D viscous MHD equations. Regularity criteria are established in terms of the pressure or the gradient of pressure, which improve the results in Y. Zhou [Regularity criteria for the 3D MHD equations in terms of the pressure, Int. J. Non-Linear Mech. 41(10) (2006), pp. 1174–1180] where additional conditions on the magnetic field are also needed. 相似文献