Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces
Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces
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DOI：
10.1016/j.matpur.2014.10.009
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发表时间：
2013-02
期刊：
影响因子：
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通讯作者：
Changsheng Dou;F. Jiang;Song Jiang;Yong-Fu Yang
中科院分区：
文献类型：
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作者：
Changsheng Dou;F. Jiang;Song Jiang;Yong-Fu Yang
证明了在有界区域Ω <$Rd（d= 2，3）中，当马赫数适当小时，可压缩热传导流体的定常Navier-Stokes方程的Dirichlet边值问题存在强解.同时，严格验证了低马赫数极限。证明中的基本思想是将方程分为两部分，一部分类似于定常不可压缩的大作用力Navier-Stokes方程，另一部分对应于定常可压缩的小作用力导热Navier-Stokes方程。通过分别处理这两部分，建立一致的马赫数先验估计，利用定常不可压Navier-Stokes方程的已知结果，建立了该方程的存在性。
We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier–Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain Ω⊂ R d (d= 2, 3), provided that the Mach number is appropriately small. At the same time, the low Mach number limit is rigorously verified. The basic idea in the proof is to split the equations into two parts, one of which is similar to the steady incompressible Navier–Stokes equations with large forces, while another part corresponds to the steady compressible heat-conductive Navier–Stokes equations with small forces. The existence is then established by dealing with these two parts separately, establishing uniform in the Mach number a priori estimates and exploiting the known results on the steady incompressible Navier–Stokes equations.