一类广义不可压Boussinesq方程组解的局部存在性及爆破准则

doi:10.6040/j.issn.1671-9352.0.2020.234

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (2): 97-102.doi: 10.6040/j.issn.1671-9352.0.2020.234

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一类广义不可压Boussinesq方程组解的局部存在性及爆破准则

侯春娟,李远飞,郭连红^*

广东财经大学华商学院数据科学学院, 广东广州 511300

发布日期:2021-01-21
作者简介:侯春娟(1983— ),女,硕士,副教授,研究方向为偏微分方程理论与应用. E-mail:houchunjuanhao@163.com*通信作者简介:郭连红(1982— ),女,硕士,副教授,研究方向为偏微分方程理论与应用. E-mail:guoat164@163.com
基金资助:
广东普通高校重点科研(自然科学)资助项目(2019KZDXM042);广东财经大学华商学院校内导师制项目(2020HSDS02)

Local existence and blow-up criterion of solutions to a class of generalised incompressible Boussinesq equations

HOU Chun-juan, LI Yuan-fei, GUO Lian-hong^*

College of Data Science, Huashang College, Guangdong University of Finance Economics, Guangzhou 511300, Guangdong, China

Published:2021-01-21

摘要/Abstract

摘要： 研究一类带黏性项、零扩散广义Boussinesq方程组局部解的存在性问题,应用正则化方法、压缩映像原理以及经典的能量估计方法,证明了带黏性项、零扩散的广义Boussinesq方程组解的局部存在性,应用Sobolev不等式获得解的一个爆破准则。研究结果能揭示一类特殊流体运动的物理现象,能更精确地反应流体的运动情况。

关键词: Boussinesq方程组, 正则化, 能量估计方法, 局部存在性

Abstract: A kind of adhesive, zero spread of the existence of the generalized local solution Boussinesq equations is considered. Using the regularization method, the compression mapping principle and the classical energy estimation method, the adhesive, zero spread of the local existence of the generalized Boussinesq equations are derived. And using the technique of Sobolev inequality, a blasting principles is obtained. The results of the study reveals a kind of special physical phenomenon of fluid movement.

Key words: Boussinesq equations, regularization, energy estimation method, local well-posedness

中图分类号:

O175.29

侯春娟,李远飞,郭连红. 一类广义不可压Boussinesq方程组解的局部存在性及爆破准则[J]. 《山东大学学报(理学版)》, 2021, 56(2): 97-102.

HOU Chun-juan, LI Yuan-fei, GUO Lian-hong. Local existence and blow-up criterion of solutions to a class of generalised incompressible Boussinesq equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 97-102.

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一类广义不可压Boussinesq方程组解的局部存在性及爆破准则

Local existence and blow-up criterion of solutions to a class of generalised incompressible Boussinesq equations

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