Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations
Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations
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DOI：
10.1002/cpa.21382
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发表时间：
2010-04
影响因子：
3
通讯作者：
Xiangdi Huang;Jing Li;Z. Xin
中科院分区：
文献类型：
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作者：
Xiangdi Huang;Jing Li;Z. Xin
我们建立了三个空间维度中等熵可压缩纳维-斯托克斯方程的柯西问题经典解的全局存在性和唯一性，初始数据具有小能量，但可能存在大振荡，常态为远场，可以是真空或非真空。允许初始密度消失，真空集合的空间测度可以是任意大；特别是初始密度甚至可以有紧凑的支撑。这些结果概括了先前关于严格远离真空的初始密度的经典解的结果，并且是可能具有大振荡并且可以包含真空状态的全局经典解的第一个结果。 © 2012 Wiley 期刊公司。
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier‐Stokes equations in three spatial dimensions with smooth initial data that are of small energy but possibly large oscillations with constant state as far field, which could be either vacuum or nonvacuum. The initial density is allowed to vanish, and the spatial measure of the set of vacuum can be arbitrarily large; in particular, the initial density can even have compact support. These results generalize previous results on classical solutions for initial densities being strictly away from vacuum and are the first for global classical solutions that may have large oscillations and can contain vacuum states. © 2012 Wiley Periodicals, Inc.