PreprintCC BY 4.0arXiv
Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy
Abstract
We prove the global existence of solutions to the Navier-Stokes equations for any divergence-free distributional initial data. The solutions are smooth in both time and space at positive times. When the initial data belong to the Sobolev spaces W−1,p for 1<p<∞, our constructed solutions are weak in the classical sense. We also characterize the distributional initial data admitting weak solutions and obtain the sharp ranges in Besov and Triebel-Lizorkin spaces.
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BibTeX
@misc{cheskidov2026global,
title = {{Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy}},
author = {Alexey Cheskidov and Hedong Hou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18797},
eprint = {2610.18797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy
AU - Alexey Cheskidov
AU - Hedong Hou
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18797
UR - https://arxiv.org/abs/2610.18797
AB - We prove the global existence of solutions to the Navier-Stokes equations for any divergence-free distributional initial data. The solutions are smooth in both time and space at positive times. When the initial data belong to the Sobolev spaces W^−1,p for 1<p<∞, our constructed solutions are weak in the classical sense. We also characterize the distributional initial data admitting weak solutions and obtain the sharp ranges in Besov and Triebel-Lizorkin spaces.
ER -