2018/12/13 by Ricardo J. Alonso, Yoshinori Morimoto, Alonso, Ricardo +5 · 2 citations
Engineering · Mathematics · #35B65 #35Q35 #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1812.05299
openalex publication_date 2018/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is obtained for both mild and strong angular singularities by combining three ingredients: the moment propagation, the spectral gap of the linearized operator, and the regularizing effect of the linearized operator when the initial data is in a Sobolev space with a negative index. A carefully designed pseudo-differential operator plays an central role in capturing the regularizing effect. Moreover, some intrinsic symmetry with respect to the collision operator and an intrinsic functional in the coercivity estimate are essentially used in the commutator estimates for the collision operator with velocity weights.