发表机构
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; University of Chinese Academy of Sciences; Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences; School of Mathematical Sciences, Dalian University of Technology（中国科学院数学与系统科学研究院; 中国科学院大学; 中国科学院数学与系统科学研究院应用数学研究所; 大连理工大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文改进了非负平面欧拉涡量支撑半径的界，去除了对数因子，得到$O(t^{1/4})$界，并证明了支撑半径平方的时间Hölder连续性。
AI 中文摘要
我们证明了具有紧支撑$L^1$初值的非负平面欧拉涡量的支撑半径满足$O(t^{1/4})$界，去除了经典限制估计中的对数因子。该结果在对称化涡量表述中成立。相互作用核的因式分解导出了高阶矩的二次卷积不等式。保留该卷积允许对有限矩和进行初等比较以控制整个支撑。我们还证明了支撑半径的平方关于时间具有指数为$1/2$的Hölder连续性。
英文摘要
We prove an $O(t^{1/4})$ bound on the support radius of nonnegative planar Euler vorticity with compactly supported $L^1$ initial data, removing the logarithmic factors from the classical confinement estimates. The result holds in the symmetrized vorticity formulation. A factorization of the interaction kernel yields a quadratic convolution inequality for high-order moments. Retaining this convolution allows an elementary comparison for finite sums of moments to control the full support. We also prove that the squared support radius is Hölder continuous in time with exponent $1/2$.
