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<p>This paper establishes blow-up criteria for strong solutions to the two-dimensional non-isothermal magnetoviscoelastic system with temperature-dependent coefficients. Under suitable regularity assumptions, we prove three main results: a Serrin-type criterion in terms of ∇<i>θ</i> and ∇<i>M</i>, its extension to Besov spaces, and a Beale-Kato-Majda-type criterion. These results provide the first systematic characterization of finite-time breakdown of solutions for this coupled system, advancing the regularity theory of non-isothermal complex fluids.</p>

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Blow-up Criteria for Non-isothermal Magnetoviscoelastic Fluids in ℝ2

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Heng Deng,
  • Guang-wu Wang

摘要

This paper establishes blow-up criteria for strong solutions to the two-dimensional non-isothermal magnetoviscoelastic system with temperature-dependent coefficients. Under suitable regularity assumptions, we prove three main results: a Serrin-type criterion in terms of ∇θ and ∇M, its extension to Besov spaces, and a Beale-Kato-Majda-type criterion. These results provide the first systematic characterization of finite-time breakdown of solutions for this coupled system, advancing the regularity theory of non-isothermal complex fluids.