TY - JOUR
T1 - Global existence for a quasilinear wave equation outside of star-shaped domains
AU - Keel, Markus
AU - Smith, Hart F.
AU - Sogge, Christopher D.
N1 - Funding Information:
1The authors were supported in part by the NSF.
PY - 2002/2/20
Y1 - 2002/2/20
N2 - We prove global existence of small-amplitude solutions of quasilinear Dirichlet-wave equations outside of star-shaped obstacles in (3 + 1)-dimensions. We use a variation of the conformal method of Christodoulou. Since the image of the space-time obstacle is not static in the Einstein diamond, our results do not follows directly from local existence theory as did Christodoulou's for the nonobstacle case. Instead, we develop weighted estimates that are adapted to the geometry. Using them and the energy-integral method we obtain solutions in the Einstein diamond minus the dime-dependent obstacle, which pull back to solutions in Minkowski space minus and obstacle.
AB - We prove global existence of small-amplitude solutions of quasilinear Dirichlet-wave equations outside of star-shaped obstacles in (3 + 1)-dimensions. We use a variation of the conformal method of Christodoulou. Since the image of the space-time obstacle is not static in the Einstein diamond, our results do not follows directly from local existence theory as did Christodoulou's for the nonobstacle case. Instead, we develop weighted estimates that are adapted to the geometry. Using them and the energy-integral method we obtain solutions in the Einstein diamond minus the dime-dependent obstacle, which pull back to solutions in Minkowski space minus and obstacle.
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U2 - 10.1006/jfan.2001.3844
DO - 10.1006/jfan.2001.3844
M3 - Article
AN - SCOPUS:0037138367
SN - 0022-1236
VL - 189
SP - 155
EP - 226
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -