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A Unidirectional Flow Problem with Radon Measure Data(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2020年03期
Page:
12-15
Research Field:
·数学·
Publishing date:

Info

Title:
A Unidirectional Flow Problem with Radon Measure Data
Author(s):
Zhou Guangfa
Department of General Courses Jiangsu Police Institute,Nanjing 210031,China
Keywords:
Radon measure; weak solutions; unidirectional flow
PACS:
35K57 35B40
DOI:
10.3969/j.issn.1001-4616.2020.03.003
Abstract:
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.

References:

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Last Update: 2020-09-15