This work concerns the existence of solution of the kinetic spinor Boltzmann equation as well as the asymptotic behavior of such solution when $ \varepsilon \to 0 $, that is when the time relaxation of the spin-flip collisions is very small in comparison to the time relaxation parameter of the collisions with no spin reversal. Due to the lack of regularity of the weak solution, the switching term $ H_\varepsilon\times M_\varepsilon $ is not stable under the weak convergences. Hence we establish new estimates of the solutions in a weighted Sobolev space of order 3.

中文翻译：

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动力学Bloch方程的宏观极限

这项工作涉及动力学自旋Boltzmann方程的解的存在以及当\ \ varepsilon \到0 $时，即当自旋翻转碰撞的时间弛豫与之相比时，这种解的渐近行为。无自旋反转的碰撞时间松弛参数。由于弱解的不规则性，切换项$ H_ \ varepsilon \ times M_ \ varepsilon $在弱收敛下不稳定。因此，我们在阶数为3的加权Sobolev空间中建立了解决方案的新估计。