Regularity properties of a generalized Oseen evolution operator in exterior domains, with applications to the Navier–Stokes initial value problem

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED
Yosuke Asami, Toshiaki Hishida
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引用次数: 0

Abstract

Consider a generalized Oseen evolution operator in 3D exterior domains, that is generated by a non-autonomous linearized system arising from time-dependent rigid motions. This was found by Hansel and Rhandi, and then the theory was developed by the second author, however, desired regularity properties such as estimate of the temporal derivative as well as the Hölder estimate have remained open. The present paper provides us with those properties together with weighted estimates of the evolution operator. The results are then applied to the Navier–Stokes initial value problem, so that a new theorem on existence of a unique strong \(L^q\)-solution locally in time is proved.

外域广义osee演化算子的正则性及其在Navier-Stokes初值问题中的应用
考虑三维外域的广义Oseen演化算子,它是由非自治线性化系统产生的,该系统是由时变刚性运动产生的。这是由Hansel和Rhandi发现的,然后该理论由第二作者发展,然而,期望的正则性,如时间导数的估计以及Hölder估计仍然是开放的。本文给出了这些性质以及演化算子的加权估计。将所得结果应用于Navier-Stokes初值问题,从而证明了局部强解\(L^q\)存在的一个新定理。
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来源期刊
CiteScore
2.00
自引率
15.40%
发文量
97
审稿时长
>12 weeks
期刊介绍: The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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