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<p>This paper concerns the Cauchy problem of the 3D magneto-viscoelastic fluids. Using the pure energy method, we prove the global well-posedness of the classical solutions with smooth initial data of small <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation> energy. Furthermore, under some additional assumptions on the initial data, we obtain the algebraic temporal decay rates of the higher-order spatial derivatives of solutions.</p>

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Global Existence and Temporal Decay for the 3D Magneto-Viscoelastic Fluids

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Chengling Li,
  • Qiao Liu

摘要

This paper concerns the Cauchy problem of the 3D magneto-viscoelastic fluids. Using the pure energy method, we prove the global well-posedness of the classical solutions with smooth initial data of small L 2 $L^{2}$ energy. Furthermore, under some additional assumptions on the initial data, we obtain the algebraic temporal decay rates of the higher-order spatial derivatives of solutions.