Updates are available Correction dated 2026-05-19

Article History

Received: 22 July 2025

Accepted: 23 February 2026

First Online: 17 March 2026

Change Date: 9 April 2026

Change Type: Update

Change Details: The original online version of this article was revised: In this article, in the Abstract section, the sentence “This work serves as a continuation of our previous paper Cao(JAMA 21:2923–2954 (2021).” should have read “This work serves as a continuation of our previous paper Cao et al. (J. Evol. Equ. 21:2923–2954 (2021)).

Change Details: In the Introduction section, the phrase "with a heat advection–diffusion equation" is duplicated in the first sentence and should read: “The classical Boussinesq approximation, which models Rayleigh–Bénard convection, consists of a system of equations coupling the three-dimensional Navier–Stokes equations with a heat advection–diffusion equation.”

Change Date: 19 May 2026

Change Type: Correction

Change Details: A Correction to this paper has been published:

Change Details: https://doi.org/10.1007/s00332-026-10263-x

Declarations

:

: The authors declare no conflict of interest.