ALEXANDRE, Radjesvarane; MORIMOTO, Yoshinori; UKAI, Seiji; XU, Chao-Jiang; YANG, Tong

doi:10.1007/s00220-011-1242-9

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ALEXANDRE, Radjesvarane
Institut de Recherche de l'Ecole Navale [IRENAV]

MORIMOTO, Yoshinori
Graduate School of Human and Environmental Studies

UKAI, Seiji
retaite [Mr.]

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Communications in Mathematical Physics. 2011, vol. 304, p. 513-581

Springer Verlag

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We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and C∞ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem.< Réduire

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Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff

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