PreprintCC BY 4.0arXiv
Periodicity and Inertial Manifolds for Navier-Stokes Flows on d-Spheres
Abstract
Consider a d-sphere 𝕊d and denote by Γ(T𝕊d) the set of all vector fields on 𝕊d. We study the Navier-Stokes equations (NSE): ∂t u + ∇u u + grad π= Δ u + div f(·, t); div u=0, for the vector field u(·, t)∈ Γ(T𝕊d), where Δ denotes the Ebin-Marsden Laplace operator defined by Δ u= div (∇ u + ∇ ut)♯, and div f(·, t) is the periodic external force. We investigate the Navier-Stokes equations in the framework of Lp-spaces over vector fields on 𝕊d and prove the existence and uniqueness of a periodic solution to such equations. Moreover, exploiting the distribution of eingenvalues of Ebin-Marsden Laplace operator we show the existence of an inertial manifold for solutions around that solution.
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BibTeX
@misc{vu2026periodicity,
title = {{Periodicity and Inertial Manifolds for Navier-Stokes Flows on $d$-Spheres}},
author = {Thi Ngoc Ha Vu and Thieu Huy Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11084},
eprint = {2610.11084},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11084},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Periodicity and Inertial Manifolds for Navier-Stokes Flows on d-Spheres
AU - Thi Ngoc Ha Vu
AU - Thieu Huy Nguyen
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11084
UR - https://arxiv.org/abs/2610.11084
AB - Consider a d-sphere 𝕊^d and denote by Γ(T𝕊^d) the set of all vector fields on 𝕊^d. We study the Navier-Stokes equations (NSE): ∂_t u + ∇_u u + grad π= Δ u + div f(·, t); div u=0, for the vector field u(·, t)∈ Γ(T𝕊^d), where Δ denotes the Ebin-Marsden Laplace operator defined by Δ u= div (∇ u + ∇ u^t)^♯, and div f(·, t) is the periodic external force. We investigate the Navier-Stokes equations in the framework of L^p-spaces over vector fields on 𝕊^d and prove the existence and uniqueness of a periodic solution to such equations. Moreover, exploiting the distribution of eingenvalues of Ebin-Marsden Laplace operator we show the existence of an inertial manifold for solutions around that solution.
ER -