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arXiv math/0501386math.AP
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全Navier-斯托克斯方程的低马赫数极限

Low Mach number limit of the full Navier-Stokes equations

T. Alazard

摘要:

本文研究了全Navier斯托克斯方程经典解的低马赫数极限。大的温度变化和热传导的综合影响占。特别是,我们考虑一般的初始数据。该方程依赖于一个小的尺度参数,导致一个奇异问题,其线性化不是一致适定的。然而,我们证明了解的存在性,并且在一定的时间间隔内一致有界,该时间间隔与(0,1)中的马赫数Ma,[1,+ \infty ]中的雷诺数Re和[1,+ \infty ]中的Peclet数Pe无关.基于索伯列夫空间中的一致估计,利用G. Metivier和S. Schochet,我们接下来证明了大项局部强收敛到零。它使我们能够严格地证明著名的正式计算中所描述的书的介绍P。L.狮子

英文摘要:

The low Mach number limit for classical solutions to the full Navier Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are accounted. In particular we consider general initial data. The equations leads to a singular problem, depending on a small scaling parameter, whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniformly bounded for a time interval which is independent of the Mach number Ma in (0,1], the Reynolds number Re in [1,+\infty] and the Peclet number Pe in [1,+\infty]. Based on uniform estimates in Sobolev spaces, and using a Theorem of G. Metivier and S. Schochet, we next prove that the large terms converge locally strongly to zero. It allows us to rigorously justify the well-known formal computations described in the introduction of the book of P.-L. Lions.

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