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

N Bournaveas; Susana Gutierrez

doi:10.1137/070698415

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

N Bournaveas, Susana Gutierrez

Mathematics

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2 Citations (Scopus)

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 language	English
Pages (from-to)	653-674
Number of pages	22
Journal	SIAM Journal on Mathematical Analysis
Volume	40
Issue number	2
DOIs	https://doi.org/10.1137/070698415
Publication status	Published - 1 Jan 2008

Keywords

kinetic transport equation
velocity-averaging lemmas
hyperbolic Sobolev spaces

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10.1137/070698415

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

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.",

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author = "N Bournaveas and Susana Gutierrez",

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doi = "10.1137/070698415",

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T1 - Averages over Spheres for Kinetic Transport Equations with Velocity Derivatives in the Right-Hand Side

AU - Bournaveas, N

AU - Gutierrez, Susana

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

KW - kinetic transport equation

KW - velocity-averaging lemmas

KW - hyperbolic Sobolev spaces

U2 - 10.1137/070698415

DO - 10.1137/070698415

M3 - Article

VL - 40

SP - 653

EP - 674

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

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

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