EconPapers    
Economics at your fingertips  
 

Large time behavior for the nonlinear dissipative Boussinesq equation

Wenhui Chen and Hiroshi Takeda

Mathematische Nachrichten, 2025, vol. 298, issue 8, 2770-2793

Abstract: In this paper, we study the nonlinear dissipative Boussinesq equation in the whole space Rn$\mathbb {R}^n$ with L1$L^1$ integrable data. As our preparations, the optimal estimates as well as the optimal leading terms for the linearized model are derived by performing the Wentzel–Kramers–Brillouin (WKB) analysis and the Fourier analysis. Then, under some conditions on the power p$p$ of nonlinearity, we demonstrate global (in time) existence of small data Sobolev solutions with different regularities to the nonlinear model by applying some fractional‐order interpolations, where the optimal growth (n=2$n=2$) and decay (n⩾3$n\geqslant 3$) estimates of solutions for large time are given. Simultaneously, we get a new large time asymptotic profile of global (in time) solutions. These results imply some influence of dispersion and dissipation on qualitative properties of solution.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.70015

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:8:p:2770-2793

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().

 
Page updated 2025-08-15
Handle: RePEc:bla:mathna:v:298:y:2025:i:8:p:2770-2793