TY - JOUR

T1 - Velocity Averaging Lemmas in Hyperbolic Sobolev Spaces for the Kinetic Transport Equation with Velocity Field on the Sphere

AU - Bournaveas, Nikolaos

AU - Wang, Hua

PY - 2009/2

Y1 - 2009/2

N2 - 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 derivative(t)f + upsilon/|upsilon| del(x)f = g(0) + del(upsilon) . g(1). Here v is allowed to vary in the whole space Rd and the velocity field a(upsilon) = upsilon/|upsilon| lies on the unit sphere. We work in dimensions d >= 3 and, in contrast with [6, 8], we allow right-hand sides with velocity derivatives in any direction and not necessarily tangential to the sphere.

AB - 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 derivative(t)f + upsilon/|upsilon| del(x)f = g(0) + del(upsilon) . g(1). Here v is allowed to vary in the whole space Rd and the velocity field a(upsilon) = upsilon/|upsilon| lies on the unit sphere. We work in dimensions d >= 3 and, in contrast with [6, 8], we allow right-hand sides with velocity derivatives in any direction and not necessarily tangential to the sphere.

UR - http://www.scopus.com/inward/record.url?scp=61449115663&partnerID=8YFLogxK

U2 - 10.1007/s00030-008-8114-9

DO - 10.1007/s00030-008-8114-9

M3 - Article

VL - 16

SP - 131

EP - 142

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

IS - 1

ER -