Local smoothing estimates for hyperbolic and dispersive equations and applications

摘要对障碍物外的波动方程，得到了Bohartz估计.作为应用，在三维区域中证明了具有幂型非线性项的半线性波动方程在障碍物外的整体（在时间上）小解的存在性，并得到了具有时空相依变系数的波动方程的加权时空L^2估计.作为应用，证明了具有低正则性径向数据的拟线性波动方程的局部（时间）适定性的一些新结果。

Abstract Strichartz estimates have been obtained for wave equations outside obstacles. As an application, the global (in time) existence of small solutions to semilinear wave equations with power-type nonlinear terms has been proved in 3-D domain outside obstacles.Weighted space-time L^2 estimates have been also obtained for wave equations with space-time dependent variable coefficients. As an application, some new results on local (in time) wellposedness have been proved for quasilinear wave equations with low regularity radial data.