Hardy Space and Exponential Decay of Inhomogeneous Navier-Stokes System in the 2D Global domain
Abstract
We investigate the inhomogeneous incompressible Navier-Stokes system in the 2D global domain with zero initial total momentum, allowing vacuum and densities with finite moments but not necessarily compact support. Exploiting the cancellation structure inherent in the 2D equations along with spatial moment bounds on the density, we derive that the inertial force belongs to the Hardy space and establish weighted Stokes estimates through endpoint Hardy-Littlewood-Sobolev inequalities. These estimates identify the far-field velocity and control the remainder, leading to uniform exponential decay of the velocity throughout global domains. Combined with higher order regularity bounds, we establish the global well-posedness of strong solutions for the density-dependent viscosity case, and prove the uniform regularity of flow maps for measurable density patches in the constant viscosity model.
Related
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BibTeX
@misc{fan2026hardy,
title = {{Hardy Space and Exponential Decay of Inhomogeneous Navier-Stokes System in the 2D Global domain}},
author = {Xinyu Fan and Boqiang Lv and Xue Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04884},
eprint = {2610.04884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04884},
}
RIS
TY - UNPB
TI - Hardy Space and Exponential Decay of Inhomogeneous Navier-Stokes System in the 2D Global domain
AU - Xinyu Fan
AU - Boqiang Lv
AU - Xue Wang
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04884
UR - https://arxiv.org/abs/2610.04884
AB - We investigate the inhomogeneous incompressible Navier-Stokes system in the 2D global domain with zero initial total momentum, allowing vacuum and densities with finite moments but not necessarily compact support. Exploiting the cancellation structure inherent in the 2D equations along with spatial moment bounds on the density, we derive that the inertial force belongs to the Hardy space and establish weighted Stokes estimates through endpoint Hardy-Littlewood-Sobolev inequalities. These estimates identify the far-field velocity and control the remainder, leading to uniform exponential decay of the velocity throughout global domains. Combined with higher order regularity bounds, we establish the global well-posedness of strong solutions for the density-dependent viscosity case, and prove the uniform regularity of flow maps for measurable density patches in the constant viscosity model.
ER -