具有Radon测度数据的单向流问题  

A Unidirectional Flow Problem with Radon Measure Data

作　　者：周光发[1] Zhou Guangfa(Department of General Courses Jiangsu Police Institute,Nanjing 210031,China)

机构地区：[1]江苏警官学院基础课教研部,江苏南京210031

出　　处：《南京师大学报（自然科学版）》2020年第3期12-15,共4页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：“十三五”江苏省重点建设学科建设工程资助项目(苏教研[2016]9号).

摘　　要：单相流问题可以从不可压流体力学中的一个简化的Boussinesq方程推导出来.Boussinesq方程由不可压Navier-Stokes方程和一个非线性热传导方程耦合而成.它在大气科学和海洋科学中有重要的应用.本文的目的是要证明具有Radon测度数据的单相流问题至少存在一个整体的弱解.我们利用正则化方法完成定理的证明.首先,构造一系列逼近的正则化解;然后,利用方程的非线性微妙结构和一个推广的Gronwall不等式,建立良好的一致估计;最后,利用标准的Aubin-Lions-Simon紧致化原理、Lebesgue控制收敛定理及非线性泛函分析中的一些结论,完成定理的证明.本文的创新之处在于充分利用方程的细微非线性结构,获得精细的一致先验估计.A unidirectional flow model is derived from a simplified Boussinesq system,which consists of a nonlinear heat equation coupled with the incompressible Navier-Stokes system.It has many important applications in atmosphere and ocean sciences.The aim of this paper is to prove the global existence of weak solutions to the unidirectional flow problem with Radon measure data.To achieve this,the regularized method is used.First,we construct the approximation strong solutions.Then,we apply a generalized Gronwall lemma to establish the uniform a priori estimates.Finally,we apply the standard compactness principle due to Aubin-Lions-Simon and thus the proof is finished.Here it should be note that the Gronwall inequality and the Lebesgue dominated convergence theorem are also used.The novelty of this paper may be lying in using the nonlinear subtle structure to obtain some fine uniform a priori estimates.

关 键 词：RADON测度 弱解 单相流 

分 类 号：K57[历史地理—历史学] B40[历史地理—世界史]