TY - JOUR
T1 - Rigorous Study of the Equilibria of Collision Kernels Appearing in the Theory of Weak Turbulence
AU - Breden, M.
AU - Desvillettes, L.
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - In this paper, we rigorously obtain all the equilibria of collision kernels of type “two particles give two particles” appearing in weak turbulence theory under very general assumptions, thus completing the “equality case” in Boltzmann’s H-theorem for those models. We also provide some rigorous results for collision kernels of type “two particles give one particle”, under assumptions which include some of the most classical kernels of this type. The method of proof is inspired by the quantitative estimates obtained for the Landau equation in (J Funct Anal 269(5): 1359–1403, 2015).
AB - In this paper, we rigorously obtain all the equilibria of collision kernels of type “two particles give two particles” appearing in weak turbulence theory under very general assumptions, thus completing the “equality case” in Boltzmann’s H-theorem for those models. We also provide some rigorous results for collision kernels of type “two particles give one particle”, under assumptions which include some of the most classical kernels of this type. The method of proof is inspired by the quantitative estimates obtained for the Landau equation in (J Funct Anal 269(5): 1359–1403, 2015).
U2 - 10.1007/s00205-019-01441-1
DO - 10.1007/s00205-019-01441-1
M3 - Article
AN - SCOPUS:85070194048
SN - 0003-9527
VL - 235
SP - 1151
EP - 1176
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -