AVERAGES OVER SPHERES FOR KINETIC TRANSPORT EQUATIONS WITH VELOCITY DERIVATIVES IN THE RIGHT-HAND SIDE

被引：2
|
作者：
Bournaveas, Nikolaos [1 ]
Gutierrez, Susana [2 ]
机构：
[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland
[2] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2008年 / 40卷 / 02期
关键词：
velocity-averaging lemmas; kinetic transport equation; hyperbolic Sobolev spaces;
D O I：
10.1137/070698415
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：653 / 674
页数：22
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