PreprintCC BY 4.0arXiv
Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data
Abstract
Given 0<a<1 and any C1, divergence-free, (−a)-homogeneous vector field u0 on the punctured plane, we construct a forward self-similar solution of the two-dimensional incompressible Euler equations on the plane with initial datum u0. No smallness or sign condition is required. The solution is obtained as a vanishing-dissipation limit of hypodissipative self-similar profiles. The key estimate is a uniform vorticity profile bound in the critical Lorentz space L2/(1+a),∞. The resulting velocity has locally finite energy and converges strongly to u0 locally in L2 as time approaches zero. The vorticity preserves its distribution function and converges strongly to the initial vorticity locally in L2/(1+a)− as time approaches zero.
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BibTeX
@misc{choi2026selfsimilar,
title = {{Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data}},
author = {Hyungjun Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.19700},
eprint = {2607.19700},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19700},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data
AU - Hyungjun Choi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2607.19700
UR - https://arxiv.org/abs/2607.19700
AB - Given 0<a<1 and any C^1, divergence-free, (−a)-homogeneous vector field u_0 on the punctured plane, we construct a forward self-similar solution of the two-dimensional incompressible Euler equations on the plane with initial datum u_0. No smallness or sign condition is required. The solution is obtained as a vanishing-dissipation limit of hypodissipative self-similar profiles. The key estimate is a uniform vorticity profile bound in the critical Lorentz space L^2/(1+a),∞. The resulting velocity has locally finite energy and converges strongly to u_0 locally in L^2 as time approaches zero. The vorticity preserves its distribution function and converges strongly to the initial vorticity locally in L^2/(1+a)− as time approaches zero.
ER -