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1.
S. J. Montgomery-Smith 《Israel Journal of Mathematics》1989,67(1):123-128
We show that the canonical embeddingC(K) →L
Φ(μ) has Gaussian cotypep, where μ is a Radon probability measure onK, and Φ is an Orlicz function equivalent tot
p(logt)
p/2 for larget. 相似文献
2.
C. Chicone Y. Latushkin S. Montgomery-Smith 《Communications in Mathematical Physics》1995,173(2):379-400
The spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in the space of continuous divergence free vector fields on a compact Riemannian manifold are described. We prove that the spectrum of the kinematic dynamo operator is exactly one vertical strip whose boundaries can be determined in terms of the Lyapunov-Oseledets exponents with respect to all ergodic measures for the Eulerian flow. Also, we prove that the spectrum of the corresponding group is obtained from the spectrum of its generator by exponentiation. In particular, the growth bound for the group coincides with the spectral bound for the generator.supported by the NSF grant DMS-9303767supported by the NSF grant DMS-9400518 and by the Summer Research Fellowship of the University of Missourisupported by the NSF grant DMS-9201357 相似文献
3.
Both authors were supported by grants from the National Science Foundation 相似文献
4.
Stephen Montgomery-Smith 《Proceedings of the American Mathematical Society》1996,124(8):2433-2437
A new proof of a result of Lutz Weis is given, that states that the stability of a positive strongly continuous semigroup on may be determined by the quantity . We also give an example to show that the dichotomy of the semigroup may not always be determined by the spectrum .
5.
Stephen Montgomery-Smith 《Proceedings of the American Mathematical Society》2001,129(10):3025-3029
We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so-called semigroup method for the Navier-Stokes equation. We also consider the possibility of existence of solutions with initial data in the Besov space . We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.
6.
7.
Stephen Montgomery-Smith 《Israel Journal of Mathematics》2002,131(1):51-60
LetX
1,X
2, …,X
n
be a sequence of independent random variables, letM be a rearrangement invariant space on the underlying probability space, and letN be a symmetric sequence space. This paper gives an approximate formula for the quantity ‖‖(X
i
)‖
N
‖
M
wheneverL
q
embeds intoM for some 1≤q<∞. This extends work of Johnson and Schechtman who tackled the case whenN=ℓ
p
, and recent work of Gordon, Litvak, Schütt and Werner who obtained similar results for Orlicz spaces.
The author was partially supported by NSF grant DMS 9870026, and a grant from the Research Office of the University of Missouri. 相似文献
8.
We precisely evaluate the operator norm of the uncentred HardyLittlewoodmaximal function on Lp(R1). Consequently, we compute the operatornorm of the strong maximal function on Lp(Rn),and we observe that the operator norm of the uncentred HardyLittlewoodmaximal function over balls on Lp(Rn) grows exponentially asn. 1991 Mathematics Subject Classification 42B25. 相似文献
9.
Stephen Montgomery-Smith David Jack Douglas E. Smith 《ournal of non Newtonian Fluid Mechanics》2011,166(7-8):343-353
Jeffery’s equation with diffusion is widely used to predict the motion of concentrated fiber suspensions in flows with low Reynold’s numbers. Unfortunately, the evaluation of the fiber orientation distribution can require excessive computation, which is often avoided by solving the related second order moment tensor equation. This approach requires a ‘closure’ that approximates the distribution function’s fourth order moment tensor from its second order moment tensor. This paper presents the Fast Exact Closure (FEC) which uses conversion tensors to obtain a pair of related ordinary differential equations; avoiding approximations of the higher order moment tensors altogether. The FEC is exact in that when there are no fiber interactions, it exactly solves Jeffery’s equation. Numerical examples for dense fiber suspensions are provided with both a Folgar–Tucker (1984) [3] diffusion term and the recent anisotropic rotary diffusion term proposed by Phelps and Tucker (2009) [9]. Computations demonstrate that the FEC exhibits improved accuracy with computational speeds equivalent to or better than existing closure approximations. 相似文献
10.
Stephen Montgomery-Smith 《Applications of Mathematics》2005,50(5):451-464
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin
or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac-like inequalities. As part
of our methods, we give a different approach to a priori estimates of Foias, Guillope and Temam.
The author was partially supported by an NSF grant. 相似文献