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徐哲峰 《数学的实践与认识》2006,36(3):249-251
对于任意实数x∈(1,∞),定义S(x)=min{m∈Nx≤m!};x∈[1,∞),S*(x)=max{m∈Nm!≤x}.主要目的是研究这两个函数的渐近性质,并给出了它们的渐近公式. 相似文献
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徐哲峰 《数学的实践与认识》2006,(3)
对于任意实数x∈(1,∞),定义S(x)=m in{m∈N∶x m!};x∈[1,∞),S*(x)=m ax{m∈N∶m!x}.主要目的是研究这两个函数的渐近性质,并给出了它们的渐近公式. 相似文献
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Summary In addition to obtaining sufficient conditions for continuability of solutions of x″ + q(t)f(x)=r(t), some sufficient conditions
and some necessary and sufficient conditions for boundedness are obtained. The asymptotic behavior of solutions is studied
through examination of r(t)/q(t) as t → ∞.
Supported by Mississippi State University Biological and Physical Sciences Research Institute.
Entrata in Redazione il 6 febbraio 1973. 相似文献
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G. V. Sandrakov 《Journal of Mathematical Sciences》2007,143(4):3377-3385
We prove statements on asymptotic estimates of solutions of nonstationary Navier-Stokes equations with periodic data rapidly
oscillating with respect to the spatial variables when the oscillations are zero in mean. A viscosity coefficient is also
considered as a positive parameter in the equations. In the general case, the proved estimates are realistic whenever the
viscosity coefficient is not too small in comparison with some power of the parameter specifying the period of data oscillations.
In particular, such estimates are valid for Kolmogorov flow with Reynolds number not too large. We formulate conditions under
which the asymptotics for velocity fields can contain rapidly oscillating terms.
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 309–322, 2007. 相似文献
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On Leray's self-similar solutions of the Navier-Stokes equations 总被引:4,自引:0,他引:4
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In this paper, we obtain sharp estimates for strong solutions of functional differential equations of neutral type. Our result
is closely connected with our previous results devoted to the initial-value problem for above-mentioned equations in the scale
of Sobolev spaces. To obtain our estimates of the solutions, we essentially use Riesz basis properties of the system of exponential
solutions. The fact that they form a Riesz basis is one of the main results of this article.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 15, Differential and Functional Differential Equations. Part 1, 2006. 相似文献
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Maria Carmela Lombardo 《Rendiconti del Circolo Matematico di Palermo》2001,50(2):299-311
We consider the time dependent incompressible Navier-Stokes equations on an half plane. For analytic initial data, existence and uniqueness of the solution are proved using the Abstract Cauchy-Kovalevskaya Theorem in Banach spaces. The time interval of existence is proved to be independent of the viscosity. 相似文献
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We obtain improved regularity criteria for the axisymmetric weak solutions of the three dimensional Navier-Stokes equations
with nonzero swirl. In particular we prove that the integrability of single component of vorticity or velocity fields, in
terms of norms with zero scaling dimension give sufficient conditions for the regularity of weak solutions. To obtain these
criteria we derive new a priori estimates for the axisymmetric smooth solutions of the Navier-Stokes equations.
Received: 11 April 2000; in final firm: 26 November 2000 / Published online: 28 February 2002 相似文献
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Cheng He 《Journal of Functional Analysis》2004,211(1):153-162
In this paper, we study the partial regularity of the general weak solution u∈L∞(0,T;L2(Ω))∩L2(0,T;H1(Ω)) to the Navier-Stokes equations, which include the well-known Leray-Hopf weak solutions. It is shown that there is a absolute constant ε such that for the weak solution u, if either the scaled local Lq(1?q?2) norm of the gradient of the solution, or the scaled local ) norm of u is less than ε, then u is locally bounded. This implies that the one-dimensional Hausdorff measure is zero for the possible singular point set, which extends the corresponding result due to Caffarelli et al. (Comm. Pure Appl. Math. 35 (1982) 717) to more general weak solution. 相似文献