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Global regularity of the Navier-Stokes equation on thin three dimensional domains with periodic boundary conditions
This paper gives another version of results due to Raugel and Sell, and
similar results due to Moise, Temam and Ziane, that state the following: the
solution of the Navier-Stokes equation on a thin 3 dimensional domain with
periodic boundary conditions has global regularity, as long as there is some
control on the size of the initial data and the forcing term, where the control
is larger than that obtainable via ``small data'' estimates. The approach taken
is to consider the three dimensional equation as a perturbation of the equation
when the vector field does not depend upon the coordinate in the thin
direction.Comment: Also available at http://math.missouri.edu/~stephen/preprint
Nasa university program review conference. summary report, mar. 1 - 3, 1965
The purpose of the NASA University Program Review Conference was to describe the nature of the Program, the manner in which it is being conducted, the results that it is producing, and the impact it may be having. The presentations, except for some expository papers by NASA offi- cials, were made by members of the university and nonprofit community. ference message as it has come to me, a university professor spending a year in making a study of NASA-University relations under a NASA contract with my institution. In preparing the report, my guiding principle has been to try to maximize its usefulness by making it accurate, brief, and prompt. These qualities are largely incompatible, and I am sure that the result of my search for an optimum compromise will please no one. Open editorializing is mainly confined to a brief section constituting my Evaluation of Program. The complete transcript will shortly be available, to stand as the authoritative source for statements that anyone may wish to attribute to the speakers
Analytic measures and Bochner measurability
Let be a -algebra over , and let denote
the Banach space of complex measures. Consider a representation for
acting on . We show that under certain, very weak
hypotheses, that if for a given and all the
map is in , then it follows that the
map is Bochner measurable. The proof is based upon the idea
of the Analytic Radon Nikod\'ym Property.
Straightforward applications yield a new and simpler proof of Forelli's main
result concerning analytic measures ({\it Analytic and quasi-invariant
measures}, Acta Math., {\bf 118} (1967), 33--59)
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