Global Spherically Symmetric Classical Solution to Compressible Navier-Stokes Equations with Large Initial Data and Vacuum
Global Spherically Symmetric Classical Solution to Compressible Navier-Stokes Equations with Large Initial Data and Vacuum
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DOI：
10.1137/110836663
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
S. Ding;Huanyao Wen;Lei Yao;Changjiang Zhu
中科院分区：
文献类型：
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作者：
S. Ding;Huanyao Wen;Lei Yao;Changjiang Zhu
本文在Rn(n>；=2)的有界域或域外得到了真空可压缩等熵N-S方程整体球对称经典解的存在唯一性的一个结果。在这里，初始数据可能很大。此外，解的正则性好于[H.J.Choe和H.Kim，Math]中的结果。方法应用。科学，28(2005)，第1-28页；Y.Cho和H.Kim，Manuscripta Math.120(2006)，第91-129页；丁少杰，温海亚，和朱振杰，J.微分方程式，251(2011)，1696-1725页].分析是基于一些新的数学技术和一些新的有用能量估计。推广了Choe和Kim，Cho和Kim，Ding，wen和朱的工作，分别得到了整体径向对称强解、三维局部经典解和一维整体经典解。本文首次证明了具有大初值的高维真空整体经典解的存在性
In this paper, we obtain a result on the existence and uniqueness of global spherically symmetric classical solutions to the compressible isentropic Navier-Stokes equations with vacuum in a bounded domain or exterior domain {\Omega} of Rn(n >= 2). Here, the initial data could be large. Besides, the regularities of the solutions are better than those obtained in [H.J. Choe and H. Kim, Math. Methods Appl. Sci., 28 (2005), pp. 1-28; Y. Cho and H. Kim, Manuscripta Math., 120 (2006), pp. 91-129; S.J. Ding, H.Y.Wen, and C.J. Zhu, J. Differential Equations, 251 (2011), pp. 1696-1725]. The analysis is based on some new mathematical techniques and some new useful energy estimates. This is an extension of the work of Choe and Kim, Cho and Kim, and Ding, Wen, and Zhu, where the global radially symmetric strong solutions, the local classical solutions in three dimensions, and the global classical solutions in one dimension were obtained, respectively. This paper can be viewed as the first result on the existence of global classical solutions with large initial data and vacuum in higher dimension