In:
Journal of Mathematics, Hindawi Limited, Vol. 2023 ( 2023-8-31), p. 1-14
Abstract:
This paper focuses on the global existence and time-decay rates of the strong solution for the Boussinesq system with full viscosity in R n for n ≥ 3 . Under the initial assumption of θ 0 , u 0 ∈ L n / 3 × L n with a small norm, and n 〉 3 or n = 3 and θ 0 ∈ L r 0 for some r 0 〉 1 , global existence and uniqueness of the strong solution θ , u for the Boussinesq system is established. This solution is proven to obey the following estimates: θ t r ≤ C t − 3 − n / p / 2 for n / 3 ≤ p 〈 ∞ , u t p ≤ C t − 1 − n / q / 2 for n ≤ q ≤ ∞ , ∇ θ t p ≤ C t − 3 − n / p / 2 − 1 / 2 and ∇ 2 θ t p = O t − n 1 / r − 1 / p / 2 − 1 as t ⟶ ∞ for r ≤ p 〈 n / 2 , and ∇ u t q ≤ C t − 1 − n / q / 2 − 1 / 2 and ∇ 2 u t q = O t − n 1 / r − 1 / q / 2 − 1 as t ⟶ ∞ for n ≤ q 〈 2 n , where r = n / 3 if n 〉 3 and 1 〈 r 〈 min r 0 , n / 2 if n = 3 .
Type of Medium:
Online Resource
ISSN:
2314-4785
,
2314-4629
DOI:
10.1155/2023/6512823
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2023
detail.hit.zdb_id:
2717090-1
