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<p>The aim of the paper is to consider the asymptotic dynamics of weak solutions for 2D MHD equations with delay terms on unbounded domains. First, we propose some appropriate assumptions of the delay terms and establish the existence and uniqueness of weak solutions. Then, the process <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2103_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>U</mi> <mo stretchy="false">(</mo> <mo>⋅</mo> <mo>,</mo> <mo>⋅</mo> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$U(\cdot ,\cdot )$</EquationSource> </InlineEquation> generated by the weak solutions is constructed. Finally, using the energy method and Arzelà–Ascoli theorem, we can establish the compactness of the process; furthermore, we prove the existence of a compact pullback attractor for the system.</p>

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Pullback attractors for 2D MHD equations with delays on unbounded domains

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  • 发表日期：

    2025年8月5日

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  • Xiaoya Song

摘要

The aim of the paper is to consider the asymptotic dynamics of weak solutions for 2D MHD equations with delay terms on unbounded domains. First, we propose some appropriate assumptions of the delay terms and establish the existence and uniqueness of weak solutions. Then, the process U ( ⋅ , ⋅ ) $U(\cdot ,\cdot )$ generated by the weak solutions is constructed. Finally, using the energy method and Arzelà–Ascoli theorem, we can establish the compactness of the process; furthermore, we prove the existence of a compact pullback attractor for the system.