Global parametrices and dispersive estimates for variable coefficient wave equations

被引：53

作者：

Metcalfe, Jason ^{[1
]}

Tataru, Daniel ^{[2
]}

机构：

[1] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

MATHEMATISCHE ANNALEN | 2012年 / 353卷 / 04期

关键词：

2ND-ORDER HYPERBOLIC OPERATORS; NONSMOOTH COEFFICIENTS; SCHRODINGER-EQUATIONS; SMOOTHING PROPERTIES; STRICHARTZ; INEQUALITY; EXISTENCE; EXTERIOR; METRICS; DECAY;

D O I：

10.1007/s00208-011-0714-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we consider variable coefficient time dependent wave equations in . Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C (2) metrics which satisfy a weak asymptotic flatness condition at infinity.

引用

页码：1183 / 1237

页数：55

共 39 条

[1] On the Morawetz - Keel-Smith-Sogge inequality for the wave equation on a curved background [J].

Alinhac, Serge .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2006, 42 (03) :705-720

[2] On global Strichartz estimates for non-trapping metrics [J].

Bouclet, Jean-Marc ;

Tzvetkov, Nikolay .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (06) :1661-1682

[3] LP-LP' ESTIMATES FOR WAVE-EQUATION [J].

BRENNER, P .

MATHEMATISCHE ZEITSCHRIFT, 1975, 145 (03) :251-254

[4]

CONSTANTIN P, 1987, CR ACAD SCI I-MATH, V304, P407

[5] Microlocal dispersive smoothing for the Schrodinger equation [J].

Craig, W ;

Kappeler, T ;

Strauss, W .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1995, 48 (08) :769-860

[6]

Delort J.-M., 1992, FBI TRANSFORMATION 2

[7] Smoothing effects for Schrodinger evolution equation and global behavior of geodesic flow [J].

Doi, S .

MATHEMATISCHE ANNALEN, 2000, 318 (02) :355-389

[8] THE UNCERTAINTY PRINCIPLE [J].

FEFFERMAN, CL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 9 (02) :129-206

[9]

Folland G.B., 1989, Annals of Mathematics Studies

[10] SMOOTHING PROPERTIES AND RETARDED ESTIMATES FOR SOME DISPERSIVE EVOLUTION-EQUATIONS [J].

GINIBRE, J ;

VELO, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 144 (01) :163-188

← 1 2 3 4 →