无旋双旋转欧拉流的涡量增长上界
On the upper bound for the vorticity growth of bi-rotational Euler flows without swirl
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中文总结 AI 辅助
针对d≥4的无旋双旋转欧拉流，研究得到Yudovich型解的局部适定性及d≤6时的全局适定性，明确其涡量增长速率与无旋轴对称流一致。
中文摘要 AI 辅助
对于维度d≥4，我们研究ℝᵈ中具有双旋转对称性且无旋的不可压缩欧拉流。首个结果给出Yudovich型解的局部适定性，第二个结果给出d≤6时的全局适定性。特别地，该结果表明涡量最大值的增长速率与无旋轴对称流的增长速率一致，该速率由第二作者与Jeong（Arch. Ration. Mech. Anal. 249(3):32, 2025）以及Shao-Wei-Zhang（Acta Math. Sin. (Engl. Ser.), 42(3):663-679, 2026）的论文得到。
英文摘要
For $d\geq 4$, we consider incompressible Euler flows in $\mathbb{R}^{d}$ with bi-rotational symmetry and without swirl. Our first result gives the local wellposedness of the Yudovich-type solution. The second result provides global wellposedness up to $d\leq 6$. In particular, it shows that the rate of growth of the vorticity maximum coincides with the rate from axisymmetric flows without swirl, which was obtained in the paper by the second author and Jeong (Arch. Ration. Mech. Anal. 249(3):32, 2025) and Shao--Wei--Zhang (Acta Math. Sin. (Engl. Ser.), 42(3):663-679, 2026).
