Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum
Morimoto, Yoshinori ; Yang, Tong
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015), p. 429-442 / Harvested from Numdam
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Nous justifions l'effet régularisant pour les solutions à valeurs mesures de l'équation de Boltzmann spatialement homogène dans le cas des molécules maxwelliennes. Il s'agit de la première preuve rigoureuse de l'effet régularisant pour toutes données initiales à valeurs mesures sauf la masse de Dirac seule, ce qui donne la description optimale de la regularité des solutions en temps positif à causée par la singularité dans le noyau de collision. Le principal ingrédient nouveau dans la preuve est l'introduction d'unc inégalité de coercivité dégénérée par rapport au temps en utilisant l'analyse microlocale.

We justify the smoothing effect for measure valued solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure valued initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.

Publié le : 2015-01-01
DOI : https://doi.org/10.1016/j.anihpc.2013.12.004
Classification:  35Q20,  76P05,  35H20,  82B40,  82C40 
@article{AIHPC_2015__32_2_429_0,
     author = {Morimoto, Yoshinori and Yang, Tong},
     title = {Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {32},
     year = {2015},
     pages = {429-442},
     doi = {10.1016/j.anihpc.2013.12.004},
     zbl = {1321.35125},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2015__32_2_429_0}
}

Morimoto, Yoshinori; Yang, Tong. Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) pp. 429-442. doi : 10.1016/j.anihpc.2013.12.004. http://gdmltest.u-ga.fr/item/AIHPC_2015__32_2_429_0/

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