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1.
Henggeng Wang 《Mathematische Nachrichten》2009,282(5):774-787
In this paper, the author establishes the decomposition of Morrey type Besov–Triebel spaces in terms of atoms and molecules concentrated on dyadic cubes, which have the same smoothness and cancellation properties as those of the classical Besov–Triebel spaces. The results extend those of M. Frazier, B. Jawerth for Besov–Triebel spaces and those of A. L. Mazzucato for Besov–Morrey spaces (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R3. We show that if0 T +∞ is the maximal time interval for the unique smooth solution u ∈ C∞([0, T), R3),then |u| + |▽d| /∈ Lq([0, T ], Lp(R3)), where p and q safisfy the Ladyzhenskaya-Prodi-Serrin's condition:3p+2q= 1 and p ∈(3, +∞]. 相似文献
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In this paper, we are concerned with the Cauchy problem for the density‐dependent incompressible flow of liquid crystals in thewhole space (N ≥ 2).We prove the localwell‐posedness for large initial velocity field and director field of the system in critical Besov spaces if the initial density is close to a positive constant. We show also the global well‐posedness for this system under a smallness assumption on initial data. In particular, this result allows us to work in Besov space with negative regularity indices, where the initial velocity becomes small in the presence of the strong oscillations. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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This paper is concerned with the time-periodic solution to the simplified incompressible nematic liquid crystal equation. We prove the existence of the time-periodic solution of this equation with small external forces g1 and g2, satisfying the T-periodic conditions gj(t)=gj(t+T) for j=1,2 in weighted Sobolev spaces. 相似文献
6.
Sadek Gala Yoshihiro Sawano Hitoshi Tanaka 《Mathematical Methods in the Applied Sciences》2012,35(11):1321-1334
In this work, we are interested in the study of regularity for the three‐dimensional magneto‐micropolar fluid equations in Orlicz–Morrey spaces. If the velocity field satisfies or the gradient field of velocity satisfies then we show that the solution remains smooth on [0,T]. In view of the embedding with 2 < p < 3 ∕ r and P > 1, we see that our result extends the result of Yuan and that of Gala. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
Qiao Liu 《Applicable analysis》2017,96(6):897-924
We use a general energy method recently developed by [Guo Y, Wang Y. Decay of dissipative equations and negative sobolev spaces. Commun. Partial Differ. Equ. 2012;37:2165–2208.] to prove the global existence and temporal decay rates of solutions to the three-dimensional compressible nematic liquid crystal flow in the whole space. In particular, the negative Sobolev norms of solutions are shown to be preserved along time evolution, and then the optimal decay rates of the higher order spatial derivatives of solutions are obtained by energy estimates and the interpolation inequalities. 相似文献
8.
After establishing the molecule characterization of the Hardy–Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy–Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier–Stokes equations for the initial data in the Hardy–Morrey space ????(p?n) for q as small as possible. Here, the Hardy–Morrey space estimates for multilinear operators are important tools. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Jie Zhang;Shu Wang;Xiang Ji; 《Mathematical Methods in the Applied Sciences》2024,47(8):7046-7055
In this note, we investigate steady compressible nematic liquid crystal flows in ℝ3$$ {mathrm{mathbb{R}}}^3 $$. We establish Liouville-type theorems for smooth solutions (ρ,u,d)$$ left(rho, u,dright) $$ that fulfill specific conditions within Lorentz spaces. 相似文献
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首先, 本文利用标准的能量估计方法得到高维(3 维及以上) 的液晶流方程组小初值经典解的整体存在性. 然后, 本文运用Green 函数方法, 得到奇数维情形(3 维及以上) 该解的逐点估计. 该结果表明, 密度ρ和动量m同Navier-Stokes 方程组一样满足一般Huygens 原理, 而单位向量场d则没有这种现象, 其有着与热方程的解类似的时空估计. 相似文献