Velocity Averaging Lemmas in Hyperbolic Sobolev Spaces for the Kinetic Transport Equation with Velocity Field on the Sphere期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Velocity Averaging Lemmas in Hyperbolic Sobolev Spaces for the Kinetic Transport Equation with Velocity Field on the Sphere

Authors:	Nikolaos Bournaveas Hua Wang

Affiliation:	(1) School of Mathematics, University of Edinburgh, JCMB King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom;(2) Department of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong, 510275, P. R. China;(3) Present address: Département de Mathématiques et Applications, école Normale Supérieure, 45 rue d’Ulm, F-75230 Paris Cedex 05, France

Abstract:	We show how the methods of [6–8] can be used to prove velocity averaging lemmas in hyperbolic Sobolev spaces for the kinetic transport equation $partial_{t}f + frac {v} {\|v\|} cdot nabla_{x}f = g_{0} + nabla_nu cdot g_{1}$ . Here v is allowed to vary in the whole space ${mathbb{R}}^{d}$ and the velocity field $a(v) = frac {v} {\|v\|}$ lies on the unit sphere. We work in dimensions and, in contrast with [6, 8], we allow right-hand sides with velocity derivatives in any direction and not necessarily tangential to the sphere.

Keywords:	KeywordHeading" >Mathematics Subject Classification (2000). 82C70 35B45 35F10 35Q75
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