共查询到20条相似文献,搜索用时 15 毫秒
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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
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Yuwen Luo 《Journal of Mathematical Analysis and Applications》2010,365(2):806-802
This paper studies the regularity of generalized magneto-hydrodynamics equation on the condition 0<α=β<3/2. It will show if ∇u∈Lp,q on [0,T) with
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We prove a new scaling invariant regularity criterion for the 3D MHD equations via horizontal gradient of horizontal components of weak solutions. This result improves a recent work by Ni et al. (2012), in the sense that the assumption on the horizontal gradient of the vertical components is removed. As a byproduct, a scaling invariant regularity criterion involving vertical components of vorticity and current density is also obtained. 相似文献
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Jiahong Wu 《偏微分方程通讯》2013,38(2):285-306
For Sobolev spaces in Lipschitz domains with no imposed boundary conditions, the Aronszajn–Smith theorem algebraically characterizes coercive formally positive integro-differential quadratic forms. Recently, linear elliptic differential operators with formally positive forms have been constructed with the property that no formally positive forms for these operators can be coercive in any bounded domain. In the present article 4th order operators of this kind are shown by perturbation to have coercive forms that are (necessarily) algebraically indefinite. The perturbation here from noncoercive formally positive forms to coercive algebraically indefinite forms requires Agmon's characterization of coerciveness in smoother domains than Lipschitz. 相似文献
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In this paper, we obtain the uniqueness of the 2D MHD equations, which fills the gap of recent work by Chemin et al. (2015). 相似文献
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Jitao Liu 《Mathematical Methods in the Applied Sciences》2016,39(15):4535-4544
This paper is concerned with the regularity criterion for a class of axisymmetric solutions to 3D incompressible magnetohydrodynamic equations. More precisely, for the solutions that have the form of u = urer+uθeθ+uzez and b = bθeθ, we prove that if |ru(x,t)|≤C holds for ?1≤t < 0, then (u,b) is regular at time zero. This result can be thought as a generalization of recent results in for the 3D incompressible Navier‐Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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In this paper,we consider regularity criteria for solutions to the 3D MHD equations with incompressible conditions.By using some classical inequalities,we obtain the regularity of strong solutions to the three-dimensional MHD equations under certain sufficient conditions in terms of one component of the velocity field and the magnetic field respectively. 相似文献
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In this paper we derive some new equations and we call them MHD-Leray-alpha equations which are similar to the MHD equations. We put forward the concept of weak and strong solutions for the new equations. Whether the 3-dimensional MHD equations have a unique weak solution is unknown, however, there is a unique weak solution for the 3-dimensional MHD-Leray-alpha equations. The global existence of strong solution and the Gevrey class regularity for the new equations are also obtained. Furthermore, we prove that the solutions of the MHD-Leray-alpha equations converge to the solution of the MHD equations in the weak sense as the parameter ε in the new equations converges to zero. 相似文献
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We establish a new Liouville-type theorem for solutions of the stationary MHD equations imposing asymmetric oscillation growth conditions on the tensor-valued functions for the velocity and the magnetic field. 相似文献
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In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D(u, B) that stems from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article. 相似文献
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In this paper, we consider the steady MHD equations with inhomogeneous boundary conditions for the velocity and the tangential component of the magnetic field. Using a new construction of the magnetic lifting, we obtain existence of weak solutions under sharp assumption on boundary data for the magnetic field. 相似文献
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Zujin Zhang 《Journal of Mathematical Analysis and Applications》2011,375(2):799-802
We study the Cauchy problem for the generalized MHD equations, and prove some regularity criteria involving the integrability of ∇u in the Morrey, multiplier spaces. 相似文献
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Bin Tao Cao 《数学学报(英文版)》2012,28(1):1-36
The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with finite electrical conductivity describe the
motion of viscous electrically conducting fluids in a magnetic field. In this paper, we find eight families of solutions of
these equations by Xu’s asymmetric and moving frame methods. A family of singular solutions may reflect basic characteristics
of vortices. The other solutions are globally analytic with respect to the spacial variables. Our solutions may help engineers
to develop more effective algorithms to find physical numeric solutions to practical models. 相似文献