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<p>In this paper, we study the energy inequalities corresponding to the weak solutions of the 3D incompressible inhomogeneous Navier-Stokes equations and inhomogeneous MHD equations / Hall-MHD equations in the torus <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1948_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {T}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>, respectively. We get some new sufficient conditions by means of the Sobolev multiplier spaces and interpolation inequality, which guarantee the establishment of the energy equalities that help solve the uniqueness problem of weak solutions to the fluid dynamics equations mentioned above.</p>

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Energy Equalities of the Inhomogeneous Navier-Stokes Equations, MHD Equations and Hall-MHD Equations

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Yi Feng,
  • Weihua Wang

摘要

In this paper, we study the energy inequalities corresponding to the weak solutions of the 3D incompressible inhomogeneous Navier-Stokes equations and inhomogeneous MHD equations / Hall-MHD equations in the torus \(\mathbb {T}^{3}\) T 3 , respectively. We get some new sufficient conditions by means of the Sobolev multiplier spaces and interpolation inequality, which guarantee the establishment of the energy equalities that help solve the uniqueness problem of weak solutions to the fluid dynamics equations mentioned above.