澳门蒲京娱乐场

Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space

We establish the global in time hydrodynamic limit of Boltzmann equation to the planar rarefaction wave of compressible Euler system in three dimensional space $x\in\mathbb R^3$ for general collision kernels. Our approach is based on a generalized Hilbert expansion, and a recent $L^2$−$L^\infty$ framework. In particular, we improve the $L^2$-estimate to be a localized version because the planar rarefaction wave is indeed a one-dimensional wave which makes the source terms to be not integrable in the $L^2$ energy estimate of three dimensional problem. We also point out that the wave strength of rarefaction may be large.