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<p>This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space ℝ<sup>3</sup>. For regular initial data with <i>m</i><sub>0</sub><i>E</i><sub>0</sub> is suitable small, where <i>m</i><sub>0</sub> and <i>E</i><sub>0</sub> represent the upper bound of initial density and initial energy, we prove that if <i>ρ</i><sub>0</sub> ∈ <i>L</i><sup><i>γ</i></sup> ∩ <i>H</i><sup>3</sup> with <i>γ</i> ∈ (1, 6), then the problem possesses a unique global classical solution on ℝ<sup>3</sup> × [0, <i>T</i>] with any <i>T</i> ∈ (0, ∞). It’s worth noting that both the vacuum states and possible random largeness of initial energy are allowed.</p>

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Global classical solutions of 3D compressible micropolar fluids with far-field vacuum

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Mingyu Zhang

摘要

This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space ℝ3. For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density and initial energy, we prove that if ρ0 ∈ Lγ ∩ H3 with γ ∈ (1, 6), then the problem possesses a unique global classical solution on ℝ3 × [0, T] with any T ∈ (0, ∞). It’s worth noting that both the vacuum states and possible random largeness of initial energy are allowed.