On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
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DOI：
10.1016/j.jde.2015.01.012
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
Noboru Chikami;R. Danchin
中科院分区：
文献类型：
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作者：
Noboru Chikami;R. Danchin
研究了Rn中粘性和导热流体所满足的完全可压缩Navier-Stokes方程的Cauchy问题。我们专注于所谓的临界Besov正则性框架。在这种情况下，自然可以考虑初始密度ρ 0、速度场u 0和温度θ 0，其中a 0：= ρ 0− 1∈ B stecp，1 n p，u 0∈ B stecp，1 n p− 1和θ 0∈ B stecp，1 n p− 2。在拉格朗日坐标系下重新构造了整个系统，并将其与温度关系改为与总能量沿着流动关系，发现当空间维数n≥ 2且1< p<2n时，该系统可以在临界泛函框架下用Banach不动点定理求解.回到欧拉坐标，与[7]相比，这允许改善系统局部适定的p的范围。
We are concerned with the Cauchy problem of the full compressible Navier–Stokes equations satisfied by viscous and heat conducting fluids in R n. We focus on the so-called critical Besov regularity framework. In this setting, it is natural to consider initial densities ρ 0, velocity fields u 0 and temperatures θ 0 with a 0:= ρ 0− 1∈ B˙ p, 1 n p, u 0∈ B˙ p, 1 n p− 1 and θ 0∈ B˙ p, 1 n p− 2. After recasting the whole system in Lagrangian coordinates, and working with the total energy along the flow rather than with the temperature, we discover that the system may be solved by means of Banach fixed point theorem in a critical functional framework whenever the space dimension is n≥ 2, and 1< p< 2 n. Back to Eulerian coordinates, this allows to improve the range of p's for which the system is locally well-posed, compared to [7].