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.

引用

页码：653 / 674

页数：22

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