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<p>We study the Navier-Stokes equations on the two-dimensional torus <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="30_2025_1070_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {T}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> with a single input bilinear control term which forces the evolution to preserve hyperplanes. We reduce the problem to the solution of the Navier-Stokes system perturbed by a certain nonlinear nonlocal term and show the well-posedness of the initial value problem for such a system.</p>

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Invariant hyperplanes for 2D Navier–Stokes equations perturbed by nonlocal terms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月22日

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  • Piermarco Cannarsa,
  • Hélène Frankowska

摘要

We study the Navier-Stokes equations on the two-dimensional torus \(\mathbb {T}^2\) T 2 with a single input bilinear control term which forces the evolution to preserve hyperplanes. We reduce the problem to the solution of the Navier-Stokes system perturbed by a certain nonlinear nonlocal term and show the well-posedness of the initial value problem for such a system.