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

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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.

Original languageEnglish
Pages (from-to)131-142
Number of pages12
JournalNonlinear Differential Equations and Applications
Issue number1
Publication statusPublished - Feb 2009

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