二维简化重力两层半模型全局解的存在性和衰减率  

Global existence and decay rate of solutions for 2-D reduced gravity two and a half layer model

作　　者：杨琪萌 李自来 YANG Qimeng;LI Ziai(School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710129,China;School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710129 [2]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《纯粹数学与应用数学》2025年第1期71-88,共18页Pure and Applied Mathematics

基　　金：国家自然科学基金(11571280).

摘　　要：本文主要研究二维简化重力两层半模型解的整体存在性和大时间行为.首先假设初始数据(ρ_(10),u_(10),ρ_(20),u_(20))的H^(2)范数充分小,通过能量方法建立了整体解的存在性.另外,如果初始数据属于Besov空间B_(2,∞)^(-1),应用Fourier分频方法和Littlewood-Paley理论,在H^(2)框架下得到了解的最优衰减率.In this paper,we are concerned with the global existence and long time behavior of solutions to the two-dimensional reduced gravity two and a half layer model.Under assumption that the initial data(ρ_(10),u_(10),ρ_(20),u_(20))is small in H^(2),we establish the existence of strong solutions by energy method.Furthermore,we obtain optimal decay rate in H^(2)-framework by Fourier splitting method and the Littlewood-Paley theory if the initial data belongs to B_(2,∞)^(-1)additionally.

关 键 词：两层半模型 BESOV空间 Fourier分频方法 时间衰减率 

分 类 号：O175.2[理学—数学]