Global existence of strong solutions of Navier-Stokes equations with non-Newtonian potential for one-dimensional isentropic compressible fluids

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• 作者：Yuan Hongjun^a ; ^{hjy@jlu.edu.cn} ; Liu Hongzhi^a ; ^b ; ^{liuhz08@mails.jlu.edu.cn} ; Qiao Jiezeng^b ; Li Fanpei^b
• 关键词：Navier-Stokes equations ; isentropic compressible fluids ; global strong solutions ; vacuum ; non-Newtonian potential
• 刊名：Acta Mathematica Scientia
• 出版年：2012
• 期刊代码：1_02529602
• 类别：mt
• 出版时间：July, 2012
• 卷：32
• 期：4
• 页码：1467-1486
• 文件大小：339 K

摘要

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.