TY - JOUR

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

AU - Bournaveas, Nikolaos

AU - Gutierrez, Susana

PY - 2008

Y1 - 2008

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.

UR - http://www.scopus.com/inward/record.url?scp=61449106817&partnerID=8YFLogxK

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

SN - 0036-1410

IS - 2

ER -