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PreprintarXiv licencearXiv

An improved bound on the support diameter of nonnegative planar Euler vorticity

  • Daomin Cao
  • Junhong Fan
  • Guodong Wang
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Abstract

We prove an O(t1/4) bound on the support radius of nonnegative planar Euler vorticity with compactly supported L1 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.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026improved,
  title = {{An improved bound on the support diameter of nonnegative planar Euler vorticity}},
  author = {Daomin Cao and Junhong Fan and Guodong Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16869},
  eprint = {2609.16869},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16869},
}
RIS
TY  - UNPB
TI  - An improved bound on the support diameter of nonnegative planar Euler vorticity
AU  - Daomin Cao
AU  - Junhong Fan
AU  - Guodong Wang
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16869
UR  - https://arxiv.org/abs/2609.16869
AB  - 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.
ER  -