Averages over Spheres for Kinetic Transport Equations with Velocity Derivatives in the Right-Hand Side

Nikolaos Bournaveas, Susana Gutierrez

Research output: Contribution to journalArticlepeer-review

Abstract

We prove estimates in hyperbolic Sobolev spaces H-s,H-delta(R1+d), d >= 3, for velocity averages over spheres of solutions to the kinetic transport equation partial derivative(t)f + v . del(x)f = Omega(i,j)(v) g, where Omega(i,j)(v) g are tangential velocity derivatives of g. Our results extend to all dimensions earlier results of Bournaveas and Perthame in dimension two [J. Math. Pures Appl., 9 (2001), pp. 517-534]. We construct counterexamples to test the optimality of our results.

Original languageEnglish
Pages (from-to)653-674
Number of pages22
JournalSIAM Journal on Mathematical Analysis
Volume40
Issue number2
DOIs
Publication statusPublished - 2008

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