On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles
On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles
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DOI：
10.1090/s0002-9947-09-05053-3
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发表时间：
2008-05
影响因子：
1.3
通讯作者：
K. Hidano;Jason Metcalfe;Hart F. Smith;C. Sogge;Yi Zhou
中科院分区：
文献类型：
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作者：
K. Hidano;Jason Metcalfe;Hart F. Smith;C. Sogge;Yi Zhou
我们建立了关于非线性波动方程的小数据整体存在性的Strauss猜想，在紧障碍物的外部区域的设置中，空间维数n = 3和4。障碍物被假定为非陷阱，并假定解决方案满足沿着障碍物的边界的狄利克雷或诺依曼条件。证明的关键步骤是建立外区域上线性波动方程的某些“抽象的Eschhartz估计”。
We establish the Strauss conjecture concerning small-data global existence for nonlinear wave equations, in the setting of exterior domains to compact obstacles, for space dimensions n = 3 and 4. The obstacle is assumed to be nontrapping, and the solution is assumed to satisfy either Dirichlet or Neumann conditions along the boundary of the obstacle. The key step in the proof is establishing certain "abstract Strichartz estimates" for the linear wave equation on exterior domains.