Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier–Stokes Equation in R3

We prove two Liouville-type theorems for the stationary Navier–Stokes equations in R3 under some assumptions on 1) the growth of the Ls mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The...

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Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 27; no. 3
Main Authors Bang Jeaheang, Yang Zhuolun
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.08.2025
Subjects
Estimates
Fluid flow
Navier-Stokes equations
Pressure head
Theorems
Velocity distribution
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Summary:We prove two Liouville-type theorems for the stationary Navier–Stokes equations in R3 under some assumptions on 1) the growth of the Ls mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The main idea is to use Saint-Venant type estimates to characterize the growth of Dirichlet energy of nontrivial solutions. These assumptions are weaker than those previously known of a similar nature.
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ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-025-00941-3