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粘性项依赖于密度的完全Navier-Stokes方程强解的存在唯一性
  • ISSN号：0438-0479
  • 期刊名称：厦门大学学报(自然科学版)
  • 时间：0
  • 页码：230-240
  • 语言：中文
  • 分类：O175.2[理学—数学;理学—基础数学]
  • 作者机构：[1]厦门大学数学科学学院,福建厦门361005
  • 相关基金：基金项目：国家自然科学基金（10531020）,厦门大学985信息工程2004-2007,厦门大学新世纪优秀人才资助计划（NCETXMU）资助
  • 相关项目：流体力学中偏微分方程的某些非经典理论与方法
作者： 谭忠|尹俊平|
关键词： 完全的Navier-Stokes方程, 粘性项依赖密度, 强解存在性, 唯一性, full Navier-Stokes equations, density-dependent, existence,uniqueness, strong solution
中文摘要：

对粘性项依赖于密度的完全Navier-Stokes方程进行了研究,在Rn（n=2,3）中一个边界光滑的区域Ω上讨论该系统的.初始密度满足一个兼容性条件下,本文分别证明了具热源和不具热源时,该系统的强解的存在唯一性.本文所有方法是迭代手法,该方法主要利用线性化系统强解的存在性,然后构造原始系统的迭代系统,根据迭代系统的一致估计,最终通过迭代解序列“函数值变化的一致有界性”,得到迭代解序列自然收敛.从而避免了繁琐的紧性讨论.值得一提的是我们的初始密度容许在Ω的一个子集上是真空的.

英文摘要：

In this paper,the density-dependent full Navier-Stokes equations are discussed in ΩRn（n=2,3） with smooth boundary.And the existence and the uniqueness strong solution for this system with heat sources or without heat sources are obtained,in condition that the initial density satisfies the compatibility.As methods,the iterative methods are introduced.This method mainly use the existence of strong solution for linearized system.Then by the initial system,the iterative system is constructed,and the uniform estimates are gotten from the iterative system.Finally,for the boundary of the sequences for the iterative solution,the convergence can naturally be concluded.And the complex compact discussion is avoided.Furthermore,the vacuum of initial density may be allowed.

同期刊论文项目
流体力学中偏微分方程的某些非经典理论与方法
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期刊信息
  • 《厦门大学学报：自然科学版》
  • 中国科技核心期刊
  • 主管单位:中华人民共和国教育部
  • 主办单位:厦门大学
  • 主编：谢素原
  • 地址：厦门市思明南路422号厦门大学嘉庚三 817-819室
  • 邮编：361005
  • 邮箱：jxmu@xmu.edu.cn
  • 电话：0592-2180367 2187731
  • 国际标准刊号：ISSN：0438-0479
  • 国内统一刊号：ISSN：35-1070/N
  • 邮发代号:34-8
  • 获奖情况:
  • 多次被评为全国、华东地区、福建省的优秀科技期刊,2001年入选国家新闻出版总署评定的"中国期刊方阵",2003年获国家新闻出版总署颁发的"第二届国家科技...,2006年获国家教育部科技司颁发的"首届中国高校精...
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  • 被引量:16575