Scholarlink

<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="21_2025_926_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation>-solution locally in time is proved.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月17日

查看全文
  • Yosuke Asami,
  • Toshiaki Hishida

摘要

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 \(L^q\) L q -solution locally in time is proved.