Scholarlink

<p>We prove two Liouville-type theorems for the stationary Navier–Stokes equations in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="21_2025_941_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> under some assumptions on 1) the growth of the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="21_2025_941_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^s\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>s</mi> </msup> </math></EquationSource> </InlineEquation> mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The main idea is to use Saint-Venant type estimates to characterize the growth of Dirichlet energy of nontrivial solutions. These assumptions are weaker than those previously known of a similar nature.</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

Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier–Stokes Equation in \(\mathbb {R}^3\)

  • 期刊论文

  • 发表日期：

    2025年5月8日

查看全文
  • Jeaheang Bang,
  • Zhuolun Yang

摘要

We prove two Liouville-type theorems for the stationary Navier–Stokes equations in \(\mathbb {R}^3\) R 3 under some assumptions on 1) the growth of the \(L^s\) L s mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The main idea is to use Saint-Venant type estimates to characterize the growth of Dirichlet energy of nontrivial solutions. These assumptions are weaker than those previously known of a similar nature.