Macroscopic limit of the kinetic Bloch equation

Kamel Hamdache; Djamila Hamroun

doi:10.3934/krm.2021015

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2021, Volume 14, Issue 3: 541-570. Doi: 10.3934/krm.2021015

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Macroscopic limit of the kinetic Bloch equation

Kamel Hamdache^1, and
Djamila Hamroun^2, ,

1.
Léonard de Vinci Pôle Universitaire, Research Center, 92 916 Paris La Défense Cedex, France
2.
Laboratoire AMNEDP, Faculté de Mathématiques, Université USTHB, B. P. 32 ElAlia, Bab Ezzouar, 16111 Alger, Algérie

^* Corresponding author: Djamila Hamroun
^* Corresponding author: Djamila Hamroun

Received: October 2020

Revised: February 2021

Early access: March 2021

Published: June 2021

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Abstract

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.

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Mathematics Subject Classification: 35Q20, 76P05, 82C40.

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References

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