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 -